Passive scalars in turbulent channel flow at high Reynolds number

We study passive scalars in turbulent plane channels at computationally high Reynolds number, thus allowing us to observe previously unnoticed effects. The mean scalar profiles are found to obey a generalized logarithmic law which includes a linear correction term in the whole lower half-channel, and they follow a universal parabolic defect profile in the core region. This is consistent with recent findings regarding the mean velocity profiles in channel flow. The scalar variances also exhibit a near universal parabolic distribution in the core flow and hints of a sizeable log layer, unlike the velocity variances. The energy spectra highlight the formation of large scalar-bearing eddies with size proportional to the channel height which are caused by a local production excess over dissipation, and which are clearly visible in the flow visualizations. Close correspondence of the momentum and scalar eddies is observed, with the main difference being that the latter tend to form sharper gradients, which translates into higher scalar dissipation. Another notable Reynolds number effect is the decreased correlation of the passive scalar field with the vertical velocity field, which is traced to the reduced effectiveness of ejection event

Turbulent kinetic energy production and Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

Data available in literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (2015), Bernardini et al. (2014), Yamamoto and Tsuji (2018) and Orlandi et al. (2015) in a large range of Reynolds number have been used to find that shear parameter the ratio between the eddy turnover time and the time scale of the mean deformation (1/S), scales very well with the Reynolds number in the near-wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall. the shear parameter is linked to the flow structures, as well as the second invariant, and also this quantity presents a good scaling. It has been found that the maximum of turbulent kinetic energy production occurs in the layer with the second invariant approximately zero, that is where the unstable sheet-like structures roll-up to become rods. The decomposition of production in the contribution of elongational and compressive strain demonstrates that the two contribution present a good scaling. The perfect scaling however holds when the near-wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent channels with different type of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the normal to the wall velocity fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production. These simulations at intermediate Reynolds number indicated that in the outer region the Townsend similarity hypothesis holds

On the role of secondary motions in turbulent square duct flow

We use a direct numerical simulations (DNS) database for turbulent flow in a square duct up to bulk Reynolds number \Rey_b=40000, to quantitatively analyze the role of secondary motions on the mean flow structure. For that purpose we derive a generalized form of the identity of Fukagata, Iwamoto and Kasagi (FIK), which allows to quantify the effect of cross-stream convection on the mean streamwise velocity, wall shear stress and bulk friction coefficient. Secondary motions are found to contribute for about $6\%$ of total friction, and to act as a self-regulating mechanism of turbulence whereby wall shear stress nonuniformities induced by corners are equalized, and universality of the wall-normal velocity profiles is established. We also carry out numerical experiments whereby the secondary motions are artificially suppressed, in which case their equalizing role is partially taken by the turbulent stresses

Claraite, (Cu,Zn)15(AsO4)2(CO3)4(SO4)(OH)14·7H2O: redefinition and crystal structure

Since the beginning of the 2000s, several authors reported the occurrence of As and S as chemical components of the hydrated copper hydroxy-carbonate claraite, originally described with the formula (Cu,Zn)3(CO3)(OH)4·4H2O. Owing to the lack of knowledge about the crystal structure of this mineral, the structural role played by these chemical elements was unknown. The crystal structure of claraite has now been solved from single-crystal X-ray diffraction data by using a specimen from the marble quarries of Carrara, Apuan Alps, Tuscany, Italy. Electron-microprobe analyses gave (in wt% – average of eight spot analyses): SO3 4.00, As2O5 13.16, CuO 52.64, ZnO 9.03, CO2(calc) 9.08, H2O(calc) 12.56, total 100.47. On the basis of 15 (Cu þ Zn) and 45 O atoms per formula unit, the chemical formula of claraite could be written as (Cu12.85Zn2.15)S15.00(AsO4)2.22(CO3)4(SO4)0.97(OH)13.40·6.83H2O, ideally (Cu,Zn)15(AsO4)2(CO3)4(SO4)(OH)14·7H2O. Raman spectrometry shows bands related to bending and stretching vibrations of AsO4 and SO4 groups, as well as the stretching mode of CO3 groups and O–H bonds. The unit-cell parameters of claraite are a = 10.3343(6) A , b = 12.8212(7) A , c = 14.7889(9) A , a = 113.196(4)°, b = 90.811(4)°, g = 89.818(4)°, V = 1800.9(2) A 3, space group P1. The crystal structure has been refined to R1 = 0.111 on the basis of 6956 reflections with Fo > 4s(Fo) and 363 refined parameters. Claraite shows a layered structure, with {0 0 1} heteropolyhedral layers formed by Cuf5 and Cuf6 polyhedra as well as AsO4 and CO3 groups. These layers are stacked along c through edge-sharing Cu2f10 and Cu2f8 dimers, the former being decorated by corner-sharing SO4 groups hosted within intra-framework channels together with H2O groups. Claraite is the only known mineral showing the simultaneous occurrence of essential AsO4, CO3, and SO4 groups

Montetrisaite, a new hydroxy-hydrated copper sulfate species from Monte Trisa, Vicenza, Italy

Montetrisaite, a new hydroxy-hydrated copper sulfate mineral species from Monte Trisa, Torrebelvicino, Vicenza, in Italy, has chemical formula Cu6(SO4)(OH)10•2H2O. It is associated with galena, sphalerite, chalcopyrite, cerussite, anglesite, oethite, langite, posnjakite, linarite and redgillite. The crystals are blue, vitreous, transparent, striated vertically, with a cleavage, {001}. The diffraction pattern shows strong reflections pointing to an orthorhombic unit-cell with a 2.989(2), b 16.970(5), c 14.812(4) Å, space group Cmc21, Z = 2. The strongest reflections [d in Å(Irel)(hkl)] are: 7.45(100)(002), 3.73(35)(004), 2.788(18)(061), 2.503(14)(132) and 1.595(20)(175). In addition, very weak and diffuse reflections occur, which point to a monoclinic cell with a doubled a parameter. The crystal structure is built up of layers of edge-sharing Jahn–Teller-distorted Cu-centered octahedra, to which single SO4 groups are connected on one side. Between the layers, H2O molecules are located, and the layers are connected through hydrogen bonds. The refined average structure shows sulfate groups and H2O molecules in both their statistically possible positions; in the real structure, however, only one half of those positions can be really occupied. The new mineral is structurally related to posnjakite, wroewolfeite, langite, and spangolite. On the other hand, its structure is significantly different from that of redgillite Cu6(SO4)(OH)10•H2O, which has a very similar chemical formula

Tancaite-(Ce), ideally FeCe(MoO4)3•3H2O: description and average crystal structure

Tancaite-(Ce), ideally FeCe(MoO4)3•3H2O, is a new mineral occurring within cavities in the quartz veins which cut the granite at Su Seinargiu, Sarroch (CA), Sardinia, Italy. It is a secondary mineral formed in the oxidation zone of a sulfide ore vein. Associated minerals are quartz, muscovite, molybdenite, pyrite, and a mendozavilite-like phase. Tancaite-(Ce) is red or pale brown in colour, with a vitreous to adamantine lustre. Electron microprobe analyses give (wt %) SiO2 0.34, CaO 0.09, Fe2O3 11.29, SrO 0.02, La2O3 5.04, Ce2O3 10.35, Pr2O3 1.07, Nd2O3 3.66, Sm2O3 0.19, ThO2 2.58, UO2 0.17, MoO3 58.62, and H2O (calculated) 7.43, with a sum of 100.85, from which the empirical formula is calculated. The empirical formula Fe3+1.03(Ce0.46La0.23Nd0.16Pr0.05Sm0.01U0.01Th0.07)Σ = 0.99(Mo2.96Si0.04)Σ = 3.00O12•3H2O can be simplified as Fe3+(REE)(MoO4)3•3H2O and idealized as FeCe(MoO4)3•3H2O. The presence of H2O was confirmed by micro-Raman spectrometry (stretching and bending vibrations of O–H). The calculated density is 3.834 g cm−3. The X-ray diffraction pattern of tancaite-(Ce) is characterized by a set of strong reflections, which point to a cubic subcell with a = 6.870(1) Å and space group Pm3 ¯ m, plus a set of superstructure reflections. Tancaite-(Ce) displays a new structure type not previously reported in natural and synthetic molybdates. By considering only the strong reflections, it was possible to solve and refine its average structure (R1=0.038 for 192 unique reflections with I > 2σ(I)). The crystal structure consists of FeO6 octahedra centred at the origin of the cubic subcell and linked together through MoO4 tetrahedra by corner sharing. The Mo-centred tetrahedra are statistically distributed in four symmetry-related positions, with one-fourth occupancy. In the centre of the cubic unit cell the REE cations exhibit a 6+3 coordination, bonding six oxygen atoms and three H2O molecules, each of them being disorderly distributed in four symmetry-related positions. One of the possible supercells, with a 48-fold volume with respect to the primitive cubic small subcell, corresponded to a rhombohedral lattice, with a ≈ 19.43 and c ≈ 47.60 Å in the hexagonal setting. Several unsuccessful trials were performed to solve the real crystal structure of tancaite, by indexing the additional superstructure reflections and using their intensities to refine an ordered structural model. The new mineral has been approved by the IMA CNMNC (no. 2009-097). The name comes from Giuseppe Tanca, an Italian amateur mineralogist, who discovered the mineral and gave it to us for studying

Natural grid stretching for DNS of wall-bounded flows

We propose a natural stretching function for DNS of wall-bounded flows, which blends uniform near-wall spacing with uniform resolution in terms of Kolmogorov units in the outer wall layer. Numerical simulations of pipe flow are used to educe optimal value of the blending parameter and of the wall grid spacing which guarantee accuracy and computational efficiency as a results of maximization of the allowed time step. Conclusions are supported by DNS carried out at sufficiently high Reynolds number that a near logarithmic layer is the mean velocity profile is present. Given a target Reynolds number, we provide a definite prescription for the number of grid points and grid clustering needed to achieve accurate results with optimal exploitation of resources