Numerical Stability and Accuracy of Temporally Coupled Multi-Physics Modules in Wind Turbine CAE Tools

In this paper we examine the stability and accuracy of numerical algorithms for coupling time-dependent multi-physics modules relevant to computer-aided engineering (CAE) of wind turbines. This work is motivated by an in-progress major revision of FAST, the National Renewable Energy Laboratory's (NREL's) premier aero-elastic CAE simulation tool. We employ two simple examples as test systems, while algorithm descriptions are kept general. Coupled-system governing equations are framed in monolithic and partitioned representations as differential-algebraic equations. Explicit and implicit loose partition coupling is examined. In explicit coupling, partitions are advanced in time from known information. In implicit coupling, there is dependence on other-partition data at the next time step; coupling is accomplished through a predictor-corrector (PC) approach. Numerical time integration of coupled ordinary-differential equations (ODEs) is accomplished with one of three, fourth-order fixed-time-increment methods: Runge-Kutta (RK), Adams-Bashforth (AB), and Adams-Bashforth-Moulton (ABM). Through numerical experiments it is shown that explicit coupling can be dramatically less stable and less accurate than simulations performed with the monolithic system. However, PC implicit coupling restored stability and fourth-order accuracy for ABM; only second-order accuracy was achieved with RK integration. For systems without constraints, explicit time integration with AB and explicit loose coupling exhibited desired accuracy and stability

The solubility of platinum in silicate melt under reducing conditions: Results from experiments without metal inclusions

International audienceThe solubility of Pt in silicate melt was investigated at conditions of 2073–2573 K, 2 GPa and ∼IW −1.5 to +3.5. These are the first measurements of Pt solubility under conditions more reducing than the iron-wüstite buffer (IW) which are demonstrably free from contamination by metal-inclusions. Pt solubility increases with increasing temperature and decreasing oxygen fugacity. The ability of carbon to enhance Pt solubility under reducing conditions (3500 K. Under these conditions however, the estimated Pt/Os ratio is ∼40,000 times higher than that estimated for the PUM ( Brandon et al., 2006). Instead, the PUM composition is generated most readily by metal–silicate equilibrium at more modest temperatures (∼3100 K), followed by a late accretion of chondritic material subsequent to core formation

Abundance of highly siderophile elements in lunar basalts controlled by iron sulfide melt

The Moon accreted meteoritic material towards the end of Solar System formation. Quantification of this late accretion requires an estimation of the abundance of highly siderophile, or iron-loving, elements in the lunar mantle. As lunar mantle samples are not available, estimates are derived from lunar basalt compositions, but the melting phase relations needed to derive the mantle composition are poorly constrained. Here we present sulfur solubility measurements from laboratory experiments, combined with thermodynamic calculations, which show that the lunar basalt source is likely to be saturated in a sulfur-poor, iron-rich sulfide melt that concentrates some highly siderophile elements more than others. We found that the observed range in the ratios of highly siderophile elements in primitive lunar basalts is much smaller than expected from residual sulfide control alone. Instead, the elemental ratios are consistent with mixing between primary sulfide-saturated melts and minute (<1%) amounts of lunar regolith that contain impact debris. Although the composition of some samples suggests a highly depleted lunar mantle, the exact level of depletion is unclear, because mixing trajectories overlap at the inferred level of regolith contamination. We conclude that the composition of the lunar mantle is veiled by regolith contamination of the lunar basalts. If so, highly siderophile element abundances in lunar mantle-derived materials cannot be used to determine the mass of material accreted late onto the Moon

Experiments and models bearing on the role of chromite as a collector of platinum group minerals by local reduction

Chromite is widely recognized to act as a collector for platinum group elements (PGE), which tend to be observed as discrete grains of platinum group minerals included within magmatic chromite grains. In the course of experiments involving the re-equilibration or growth of chromite and Cr-spinel in molten silicate, we observe that platinum group minerals (PGM; including metal alloys and laurite) form at the mineral-melt interface. The formation of PGM to the extent observed requires a mechanism involving sustained transport of PGE from a source within the experiment to the site of deposition. We propose that the driving force for this process is a redox gradient developed in response to mineral growth or re-equilibration with the surrounding melt. The mechanism is local reduction within the mineral-melt interfacial region as a consequence of the selective uptake of trivalent Cr and Fe from the melt by spinel relative to the divalent species. We have modeled the transient perturbation of fO2 in a compositional boundary layer melt around spinel for both crystal growth and diffusive re-equilibration of mineral and melt. We find that metal solubilities decrease by several per cent in the silicate melt at the melt-crystal interface during crystal growth, providing the driving force for PGM formation. In magmas that are saturated with PGM, as a result of falling temperature and oxygen fugacity during spinel crystallization, nucleation of PGM will be impeded by interfacial tension everywhere except in the reduced boundary layer around spinel crystals. The resulting concentration and trapping of alloy particles in the growing chromite crystals can produce apparent bulk chromite/melt partition coefficients exceeding 20 even if there is no solid solution of PGE in the chromite. The introduction of spinel grains, initially equilibrated with a maf

Transport of metals and sulphur in magmas by flotation of sulphide melt on vapour bubbles

Emissions of sulphur and metals from magmas in Earth's shallow crust can have global impacts on human society. Sulphur-bearing gases emitted into the atmosphere during volcanic eruptions affect climate, and metals and sulphur can accumulate in the crust above a magma reservoir to form giant copper and gold ore deposits, as well as massive sulphur anomalies. The volumes of sulphur and metals that accumulate in the crust over time exceed the amounts that could have been derived from an isolated magma reservoir. They are instead thought to come from injections of multiple new batches of vapour- and sulphide-saturated magmas into the existing reservoirs. However, the mechanism for the selective upward transfer of sulphur and metals is poorly understood because their main carrier phase, sulphide melt, is dense and is assumed to settle to the bottoms of magma reservoirs. Here we use laboratory experiments as well as gas-speciation and mass-balance models to show that droplets of sulphide melt can attach to vapour bubbles to form compound drops that float. We demonstrate the feasibility of this mechanism for the upward mobility of sulphide liquids to the shallow crust. Our work provides a mechanism for the atmospheric release of large amounts of sulphur, and contradicts the widely held assumption that dense sulphide liquids rich in sulphur, copper and gold will remain sequestered in the deep crust

Immiscible shoshonitic and Fe-P-oxide melts preserved in unconsolidated tephra at El Laco volcano, Chile

The origins of apparently magmatic Fe-P-O deposits like those of the El Laco volcanic complex, Chile, with masses on the order of 1 Gt remain contentious. Previous attention has been focused largely on the high-tonnage massive magnetite bodies that form the economic mineral deposits. Extensive occurrences of unconsolidated granular Fe-P-oxide materials or their apparent metamorphic equivalents have received relatively little attention. Here we report textures and compositions of unconsolidated Fe-P-oxide materials from Laco Sur, El Laco. Unconsolidated tephra at El Laco is dominated by hematite along with subsidiary Fe-phosphates, monazite, and silica. A porous hematite bomb contains menisci of two coexisting materials. One is hydrous shoshonitic glass with perlitic texture, and the other comprises finegrained intergrowths of Fe-P-REE (rare earth element) oxides having the bulk composition of the eutectic in the system FePO4-Fe2O3 with minor S, Cl, and other components. We show by experiment that very similar compositions would have coexisted as immiscible silicate and oxide liquids at 900 °C and 1 GPa in the presence of carbonic vapor, magnetite, and quartz; both will also form anhydrous liquids at 1080 °C and 101 kPa. We infer the former existence of a phosphatic Fe-oxide magma rich in volatiles that underwent explosive degassing and consequent rapid compositional undercooling to produce the observed assemblage of Fe-oxide tephra containing small amounts of Fe-P-REE phosphates and silicate glass