Carlo Massimo Casciola

DNS of wall turbulence: dilute polymers and self-sustaining mechanisms

Several studies, both numerical and experimental, have shown that the introduction of a small amount of long chain polymers in a turbulent flow alters dramatically the length and time scales which are typical of Newtonian fluids, even though turbulence self-sustaining mechanisms remain approximately the same. In such viscoelastic flows wall turbulence regeneration is still influenced by the mean shear and by the interaction of the coherent structures which still generate low and high speed streaks, but more ordered and larger with respect to Newtonian flows. In order to gain a deeper understanding of the regeneration mechanisms and the modifications induced by the presence of the polymers, we analyze the data obtained from direct numerical simulation with a micro-rheological model for the polymers. Thus, the velocity fields have been studied together with the coupling terms in the momentum equations, i.e. the divergence of the extra-stress terms due to the polymers. The analysis seems to suggest, as main effect of the viscoelastic reaction, a quite concentrated action on bursting phenomena and a stabilization of the streaks with a related decrease in the population of the wall-layer coherent structures. In addition the correlations between velocity fluctuations and viscoelastic responses have been considered with the aim to single out the passive or the active role of the polymers in different flow locations.

Cassie–Baxter and Wenzel States on a Nanostructured Surface: Phase Diagram, Metastabilities, and Transition Mechanism by Atomistic Free Energy Calculations

In this work, we study the wetting of a surface decorated with one nanogroove by a bulk Lennard-Jones liquid at various temperatures and densities. We used atomistic simulations aimed at computing the free energy of the stable and metastable states of the system, as well as the intermediate states separating them. We found that the usual description in terms of Cassie-Baxter and Wenzel states is insufficient, as the system presents two states of the Cassie-Baxter type. These states are characterized by different curvatures of the meniscus. The measured free energy barrier separating the Cassie-Baxter from the Wenzel state (and vice versa) largely exceeds the thermal energy, attesting the existence of Cassie-Baxter/Wenzel metastabilities. Finally, we found that the Cassie-Baxter/Wenzel transition follows an asymmetric path, with the formation of a liquid finger on one side of the groove and a vapor bubble on the opposite side.

Energy cascade and spatial fluxes in wall turbulence

Real turbulent flows are difficult to classify as either spatially homogeneous or isotropic. Nonetheless these idealizations allow the identification of certain universal features associated with the small-scale motions almost invariably observed in a variety of different conditions. The single most significant aspect is a flux of energy through the spectrum of inertial scales related to the phenomenology commonly referred to as the Richardson cascade. Inhomogeneity, inherently present in near-wall turbulence, generates additional energy fluxes of a different nature, corresponding to the spatial redistribution of turbulent kinetic energy. Traditionally the spatial flux is associated with a single-point observable, namely the turbulent kinetic energy density. The flux through the scales is instead classically related to two-point statistics, given in terms of an energy spectrum or, equivalently, in terms of the second-order moment of the velocity increments. In the present paper, starting from a suitably generalized form of the classical Kolmogorov equation, a scale-by-scale balance for the turbulent fluctuations is evaluated by examining in detail how the energy associated with a specific scale of motion – hereafter called the scale energy – is transferred through the spectrum of scales and, simultaneously, how the same scale of motion exchanges energy with a properly defined spatial flux. The analysis is applied to a data set taken from a direct numerical simulation (DNS) of a low-Reynolds-number turbulent channel flow. The detailed scale-by-scale balance is applied to the different regions of the flow in the various ranges of scales, to understand how – i.e. through which mechanisms, at which scales and in which regions of the flow domain – turbulent fluctuations are generated and sustained. A complete and formally precise description of the dynamics of turbulence in the different regions of the channel flow is presented, providing rigorous support for previously proposed conceptual models.

Anisotropic clustering of inertial particles in homogeneous shear flow

Recently, clustering of inertial particles in turbulence has been thoroughly analyzed for statistically homogeneous isotropic flows. Phenomenologically, spatial homogeneity of particles configurations is broken by the advection of a range of eddies determined by the Stokes relaxation time of the particles which results in a multi-scale distribution of local concentrations and voids. Much less is known concerning anisotropic flows. Here, by addressing direct numerical simulations (DNS) of a statistically steady particle-laden homogeneous shear flow, we provide evidence that the mean shear preferentially orients particle patterns. By imprinting anisotropy on large scales velocity fluctuations, the shear indirectly affects the geometry of the clusters. Quantitative evaluation is provided by a purposely designed tool, the angular distribution function of particle pairs (ADF), which allows to address the anisotropy content of particles aggregates on a scale by scale basis. The data provide evidence that, depending on the Stokes relaxation time of the particles, anisotropic clustering may occur even in the range of scales where the carrier phase velocity field is already recovering isotropy. The strength of the singularity in the anisotropic component of the ADF quantifies the level of fine scale anisotropy, which may even reach values of more than 30% direction-dependent variation in the probability to find two close-by particles at viscous scale separation.

Scaling laws and intermittency in homogeneous shear flow

In this article we discuss the dynamical features of intermittent fluctuations in homogeneous shear flow turbulence. In this flow the energy cascade is strongly modified by the production of turbulent kinetic energy related to the presence of vortical structures induced by the shear. As a consequence, the intermittency of velocity fluctuations increases with respect to homogeneous and isotropic turbulence. By using direct numerical simulations, we show that the refined Kolmogorov similarity is broken and a new form of similarity is observed, in agreement with previous results obtained in turbulent boundary layers. We find here that the statistical properties of the energy dissipation are practically unchanged with respect to homogeneous isotropic conditions, while the increased intermittency is entirely captured in terms of the new similarity law.

Spatial development of particle-laden turbulent pipe flow

The inhomogeneity of turbulence in wall bounded flows induces the phenomenology called turbophoresis whereby inertial particles of suitable mass accumulate at the solid wall. Particles injected near the axis of a fully turbulent pipe flow, after an initial spreading phase, undergo a segregation process which eventually leads to a pseudoequilibrium distribution sufficiently downstream. Wall densities up to thousand times the reference value can be easily achieved. The process is discussed here by analyzing the direct numerical simulation (DNS) data of a spatially developing particle laden pipe flow under the assumption of dilute suspension. Development phase and asymptotic state are addressed in quantitative terms. A Shannon-like entropy is introduced to quantify the level of spreading/segregation achieved by the particle distributions along the pipe. This allows to define on a physically sound basis the length of the developing region and to summarize in a single indicator the accumulation level as a func...

Scale-by-scale budget and similarity laws for shear turbulence

Turbulent shear flows, such as those occurring in the wall region of turbulent boundary layers, show a substantial increase of intermittency in comparison with isotropic conditions. This suggests a close link between anisotropy and intermittency. However, a rigorous statistical description of anisotropic flows is, in most cases, hampered by the inhomogeneity of the field. This difficulty is absent for homogeneous shear flow. For this flow the scale-by-scale budget is discussed here by using the appropriate form of the Kaman–Howarth equation, to determine the range of scales where the shear is dominant. The resulting generalization of the four-fifths law is then used to extend to shear-dominated flows the Kolmogorov–Oboukhov theory of intermittency. The procedure leads naturally to the formulation of generalized structure functions, and the description of intermittency thus obtained reduces to the K62 theory for vanishing shear. The intermittency corrections to the scaling exponents are related to the moments of the coarse-grained energy dissipation field. Numerical experiments give indications that the dissipation field is statistically unaffected by the shear, supporting the conjecture that the intermittency corrections are universal. This observation together with the present reformulation of the theory gives a reason for the increased intermittency observed in the classical longitudinal velocity increments.

Drag reduction by polymers in turbulent channel flows: Energy redistribution between invariant empirical modes

We address the phenomenon of drag reduction by a dilute polymeric additive to turbulent flows, using direct numerical simulations (DNS) of the FENE-P model of viscoelastic flows. It had been amply demonstrated that these model equations reproduce the phenomenon, but the results of DNS were not analyzed so far with the goal of interpreting the phenomenon. In order to construct a useful framework for the understanding of drag reduction we initiate in this paper an investigation of the most important modes that are sustained in the viscoelastic and Newtonian turbulent flows, respectively. The modes are obtained empirically using the Karhunen-Loéve decomposition, allowing us to compare the most energetic modes in the viscoelastic and Newtonian flows. The main finding of the present study is that the spatial profile of the most energetic modes is hardly changed between the two flows. What changes is the energy associated with these modes, and their relative ordering in the decreasing order from the most energetic to the least. Modes that are highly excited in one flow can be strongly suppressed in the other, and vice versa. This dramatic energy redistribution is an important clue to the mechanism of drag reduction as is proposed in this paper. In particular, there is an enhancement of the energy containing modes in the viscoelastic flow compared to the Newtonian one; drag reduction is seen in the energy containing modes rather than the dissipative modes, as proposed in some previous theories.

Homogeneous isotropic turbulence in dilute polymers

arm ´ an–Howarth equation, two kinds of energy fluxes exist, namely the classical transfer term and the coupling with the polymers. Depending on the Deborah number, the response of the flow may result either in a pure damping or in the depletion of the small scales accompanied by increased fluctuations at large scale. The latter behaviour corresponds to an overall reduction of the dissipation rate with respect to an equivalent Newtonian flow with identical fluctuation intensity. The relevance of the position of the crossover scale between the two components of the energy flux with respect to the Taylor microscale of the system is discussed.

Intermittency and scaling laws for wall bounded turbulence.

Well defined scaling laws clearly appear in wall bounded turbulence, very close to the wall, where a distinct violation of the refined Kolmogorov similarity hypothesis (RKSH) occurs together with the simultaneous persistence of scaling laws. A new form of RKSH for the wall region is here proposed in terms of the structure functions of order two which, in physical terms, confirms the prevailing role of the momentum transfer towards the wall in the near wall dynamics.