Giorgio Graziani

An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers

Abstract A weakly compressible SPH scheme has been used to describe the evolution of viscous flows around blunt bodies at Reynolds numbers ranging from 10 to 2400. The simulation of such a wide range, rarely addressed to in the SPH literature, has been possible thanks to the use of a proper ghost-fluid technique and to an accurate enforcement of the boundary conditions along the solid boundaries. In this context, a new numerical technique based on previous works by Takeda et al. (1994) [48] , Marrone et al. (2011) [28] and De Leffe et al. (2011) [16] has been proposed, along with a new method for the evaluation of the global loads on bodies. Particular care has been taken to study the influence of the weakly-compressibility assumption and of different ghost-fluid techniques on the numerical results. An in-depth validation of the model has been performed by comparing the numerical outcome with experimental data from the literature and other numerical references. The influence of the domain size has been discussed in order to avoid wall side effects and, at the same time, to limit the computational costs. The convergence of the numerical solutions has been checked on both global and local quantities by choosing appropriate Reynolds-cell number.

Fast free-surface detection and level-set function definition in SPH solvers

The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two- and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples.

Crystal chemistry of the elbaite-schorl series

Abstract The crystal-chemistry of 13 elbaite-schorl tourmaline crystals from the Cruzeiro pegmatite (Minas Gerais, Brazil) was studied with a multi-analytical approach (SREF, EMPA, SIMS, MS). Effective cation radii at the Y and Z sites and site populations were refined by a minimization procedure. The results indicate that the crystals belong to the alkali group. Elbaite crystals are O2.-free at the W and V sites and show OH content at the O2 site (up to 0.2 apfu). Conversely, schorl crystals always show O2. at the W site. The main substitutional mechanism is the dehydroxylation type: YFe2+ + YFe3+ + WO → YLi + YAl + W(OH+F). The T site is characterized by TSi → TAl substitution. is linearly correlated with vacancy content in crystals with (OH + F) ≤ 4, whereas it is almost constant in crystals with OH at the O2 position. Along the series, is inversely correlated with YAl. The Z site is almost fully occupied by R3+ (with ZAl largely dominant) and the ZFetot ↔ ZAl substitution explains the inverse correlation of with ZAl. In the elbaite compositional range, lattice parameters are functions of , whereas in the schorl range they are essentially functions of . Along the whole elbaite-schorl series, both chemical substitutions and size increase of Y are far larger than those of Z. In spite of this, lattice parameters increase with as much as with . This is due to the role of the [ZO6] polyhedra, which extend along a and c to form the skeleton of the tourmaline structure. Therefore, any change in the size of Z leads to a change in the whole structure.

Fe2+ and Fe3+ quantification by different approaches and fo2 estimation for Albanian Cr-spinels

Abstract Fourteen Cr-spinels from Albanian ophiolites were examined. Fe2+/Fe3+ ratios were obtained by 57Fe Mössbauer spectroscopy (MS) and compared with ratios retrieved by electron microprobe analyses (EMPA). MS spectra were collected at both 298 K (RT) and 77 K (LT), and fitted using various interpretative models. Fe3+ contents by EMPA, calculated from spinel stoichiometry, are almost always underestimated with respect to those obtained by MS. Moreover, Fe3+ contents by MS-RT are shown to be somewhat overestimated with respect to those by MS-LT, which are proved to be the most reliable. On basis of MS results, Albanian Cr-spinels proved to be non-stoichiometric, with an oxidation degree, z, ranging from 4 to 49%. Our results indicate no dependence of z on sample provenance, but suggest a strong dependence on spinel composition. Chemical data of Albanian spinel and associated olivine were used to estimate fO₂ via oxygen geobarometry. Notably, fO₂ values calculated on basis of the EMPA data are always largely underestimated with respect to those obtained on basis of MS data. However, fO₂ values calculated on basis of MS-RT data are equal to or higher than (up to 0.2 log units) fO₂ values based on MS-LT data. The increase in fO₂ responsible for spinel oxidation was tentatively estimated to be less than one log unit for poorly oxidized samples, but up to 6 log units for the most oxidized samples.

Crystal chemistry of the axinite-group minerals: A multi-analytical approach

Abstract Sixty axinite samples from 24 localities worldwide were characterized by electron microprobe analysis (EMPA) to define the limits of compositional variation. Three samples are very close to the Mn, Fe, and Mg end-members. Temaiy (Mn,Fe2+,Mg)-compositions occur mostly in the ferroaxinite and manganaxinite fields, and are constrained by the relation Mg ≤ Fe. Core-rim chemical zoning was observed in 20 samples, with systematic enrichment of Fe in the core and Mn in the rim, independent of sample provenance. The chemical composition (including B, H, and Fe2+/Fe3+) of 17 homogeneous samples was investigated using electron-microprobe analysis, thermo-gravimetry (TG), ion microprobe (SIMS), crystal-structure refinement (SREF), and Mössbauer spectroscopy (MS). For all samples except pure manganaxinite, most of the iron is Fe2+ . The content of Fe3+ and the Fe3+/ΣFe ratio mcrease with Mn content up to 0.31 atoms per formula unit (apfu) and 0.80, respectively. Fe3+ may substitute for Al or also for divalent cations balanced by the OH deficiency: Fe3++ O2-↔ Fe2++ OH-, or Fe3+O(Fe2+OH)-1 Boron content ranges from 1.88 to 2.07 apfu (±2.5% relative) and shows an inverse relation with Si content. Direct measurement of the 5-tetraliedron size provides structural confirmation of the Si ↔ B exchange. Hydioxyl deficiency accompanies this substitution and the following coupled mechanism is proposed: Si4+ + O2- ↔ B3+ + OH-, or SiO(BOH)-1 Hydrogen content ranges from 1.7 to 2.1 apfu (±5% relative). The deficiency of OH from the stoichiometric value of 2.0 per formula unit is related directly to the number of trivalent and tetravalent cations, as OH content plays a crucial role in charge-balance relations. A revised chemical formula for the axinite-group minerals is proposed: [6][Ca(Ca1-xMnx:)(Mn, Fe2+Mg,Zn,Alu,FeV3+)Σ=1(Al2-yFey3+]2[4][(B1-zSi2)Si8]O30(OH1-w0)2 , where x≤1, u <1, ν <1, y<1, z≪1, and w=(u+ν+z).

Hydroelastic slamming response in the evolution of a flip-through event during shallow-liquid sloshing

The evolution of a flip-through event [6] upon a vertical, deformable wall during shallow-water sloshing in a 2D tank is analyzed, with specific focus on the role of hydroelasticity. An aluminium plate, whose dimensions are Froude-scaled in order to reproduce the first wet natural frequency associated with the typical structural panel of a Mark III containment system, is used. (Mark III Containment System is a membrane-type tank used in the Liquefied Natural Gas (LNG) carrier to contain the LNG. A typical structural panel is composed by two metallic membranes and two independent thermal insulation layers. The first membrane contains the LNG, the second one ensures redundancy in case of leakage.) Such a system is clamped to a fully rigid vertical wall of the tank at the vertical ends while being kept free on its lateral sides. Hence, in a 2D flow approximation the system can be suitably modelled, as a double-clamped Euler beam, with the Euler beam theory. The hydroelastic effects are assessed by cross-anal...

From a boundary integral formulation to a vortex method for viscous flows

For the numerical solution of flow problems past a solid body it is worth to consider boundary integral techniques for their inherent capability to manage efficiently the far-field boundary conditions as well as the approximation of the solid body contour. However, for the analysis of large Reynolds number flows, of major interest in the applications, several computational difficulties appear when using the integral representation for the velocity or for the vorticity field in its classical form with interpolating functions (BEM). In particular, the evaluation of the volume integrals is a serious drawback while the steepness of their kernel introduces artificial diffusion in the calculation. To satisfy the opposite requirements of the advective and of the diffusive part of the Navier-Stokes equations, we adopt an operator splitting scheme according to the Chorin-Marsden product formula (Chorin et al. 1978), together with a proper vorticity generation scheme at the solid boundary. A solution procedure based on the approximation of the vorticity field by a finite number of point vortices (PVM) follows as a natural evolution of the boundary integral formulation.The numerical results given by the two methods for the merging of two like-signed vortices in free space reveal the excessive numerical diffusion of BEM. The better accuracy of PVM is also established through the evaluation of some first integrals of motion. Several results are also reported for flows in presence of solid boundaries where the vorticity generation is crucial. In this case accurate solutions are only obtained with PVM, while BEM is even less satisfactory than in free space. Finally, the proposed vortex-like method (PVM) is tested on the classical problem of the wake behind a cylinder, in comparison with other well established techniques.

Site distribution of Fe2+ and Fe3+ in the axinite mineral group: New crystal-chemical formula

Abstract A set of nine samples of axinite, selected from 60 specimens from worldwide localities, were investigated by single-crystal X-ray diffraction, electron and ion microprobe, and 57Fe Mössbauer spectroscopy. The selected samples cover the compositional join from almost pure ferroaxinite (80%) to pure manganaxinite (95%). A new crystal-chemical formula for the axinite mineral group is proposed: VI[X1 X2 Y Z1 Z2]2IV[T1 T2 T3 T4 T5]2O30(OwOH1-w)2, where VI and IV are coordination numbers; X1 = Ca and very minor Na; X2 = Ca (in axinites) or Mn (in tinzenite); Y = Mn (in manganaxinite and tinzenite), Fe2+ (in ferroaxinite) or Mg (in magnesioaxinite), with minor Al and Fe3+; Z1 = Al and Fe3+; Z2 = Al; T1, T2, and T3 = Si; T4 = Si (and presumably very minor B); T5 = B and minor Si. Charge unbalance (w), due to heterovalent substitutions, is compensated for by O2- → OH- substitution. From ferroaxinite to manganaxinite, cell volume increases linearly from 568.70 to 573.60 Å3. This is mainly due to an increase in the mean distance from 2.220 to 2.255 Å, which is directly related to the Mn population (up to 1.89 apfu). Fe3+ concentrations, as determined by 57Fe Mössbauer spectra at 80 K, sub-regularly increase up to 0.27 apfu, and three cases are evidenced: (1) Fe3+ << Fe2+ (or no Fe3+), in ferroaxinite; (2) Fe3+ < Fe2+, in intermediate compositions, and (3) Fe3+ > Fe2+ (or only Fe3+), in manganaxinite. Chemical and structural data were co-processed via a computer minimization program to obtain the cation distribution scheme. Adopting the Hard-Sphere Model, empirical cation-oxygen distances were refined for every cation in the axinite structure. The results revealed that Fe2+ is ordered at the octahedral Y site (up to 1.61 apfu), whereas Fe3+ is ordered at the octahedral Z1 site (up to 0.26 apfu) and is almost absent in the smallest Z2 site, which is fully populated by Al. The observed Fe3+ partitioning is in agreement with the structural results, which show that the Z1 octahedron is always larger than Z2. Moreover, no Fe3+ is found at the tetrahedral sites, but Si → B substitution occurs at T5. The continuous Y dimensional increase from ferroaxinite to manganaxinite involves progressive enlargement of the edge-sharing Z1 octahedron. As a consequence, the Z1Fe3+ → Z1Al3+ substitution is structurally favored toward manganaxinite and points to a new end-member with the suggested name “ferri-manganaxinite.”

General and Specific Growth Marks in Pegmatite Beryls

Growth marks of pegmatite beryls can be divided into general and specific in relation to their types and distributions. Dislocation absence and growth bands have been recognized as general growth marks of the environment while minor element concentrations and optical anomalies as specific to the local growth medium.

Unsteady Viscous Flows about Bodies: Vorticity Release and Forces

The force (drag and lift) exerted on a body moving in a viscous fluid is expressed via the ‘free’ and ‘bound’ vorticity moments, and the role of vortex shedding is discussed. The formulation encompasses classical, inviscid flows, and leads to efficient computational methods. Numerical results for a few prototype flows are presented.