Melting Model Research Articles

Partial melting mechanisms of peraluminous felsic magmatism in a collisional orogen: An example from the Khondalite belt, North China craton

AbstractSedimentary‐derived (S‐type) granites are an important product of orogenic metamorphism, and a range of subtypes can be recognized by differences in field occurrence, mineralogy and geochemistry. These subtypes can reflect variations of initial protolith composition, partial melting reactions, pressure and temperature of anatexis, or magmatic processes that occur during ascent through the crust (e.g. mineral fractional crystallization or crustal assimilation). Together, these diverse factors complicate geological interpretation of the history of peraluminous felsic melt fractions in orogenic settings. To assess the influence of these factors, we performed integrated field investigation, petrology, geochemistry, geochronology and phase equilibrium modelling on a series of leucosomes within migmatite associated with different S‐type granites within the Khondalite belt, North China craton (NCC), which is an archetypal collisional orogen. Three types of leucosome are recognized in the east Khondalite belt: leucogranitic leucosome, K‐feldspar (Kfs)‐rich granitic leucosome and garnet (Grt)‐rich granitic leucosome. Phase equilibrium modelling of partial melting and fractional crystallization processes indicate that the leucogranitic leucosomes were mostly produced through fluid‐present melting, Kfs‐rich granitic leucosomes are produced through muscovite dehydration melting with 3 vol.% garnet fractional crystallization, and Grt‐rich granitic leucosomes are produced through biotite dehydration melting with 20–40 vol.% K‐feldspar fractional crystallization and up to 20 vol.% peritectic garnet entrainment. Mineral fractional crystallization and peritectic mineral entrainment occur in the source during melting, and play equally important roles in partial melting mechanisms in terms of affecting the geochemical compositions of granitic melts. Thus, we suggest that peraluminous felsic magmas preserved in collisional orogens are dominantly produced by fluid‐absent melting in the middle to deep continental crust, although extraction of low‐volume melt fractions from an anatectic source region at shallower depths during fluid‐present melting can also generate small amounts of S‐type granites that subsequently crystallize at high structural levels in the crust.

Simulation on paraffin melting enhancement in shell-tube phase change thermal storage equipment induced by natural convection

To enhance the thermal performance of the shell-tube phase change thermal storage equipment, the transient two-dimensional mathematical models of the RT35 melting were established. The transient evolution of temperature and velocity distribution and the effect of the positions of the inner tube on the intensity of natural convection for the RT35 and the melting times were analyzed. The results showed that the evolution process of the liquid fraction of RT35 could be divided into two stages: the natural convection stage and the conduction stage. In the natural convection stage, due to the buoyancy effect, the RT35 with high-temperature flowed upward and convectively heat transferred with the solid RT35 on the upper side of the inner tube, resulting in the promotion of the melting of RT35 on the upper side of the inner tube. With the increase in the eccentricity ratio (ε), the gradual increase in the mass of RT35 on the upper side of the inner tube enhanced the effect of natural convection on the melting of RT35, leading to a significant reduction in melting time. When the heat exchange temperature differences (ΔT) ranged between 9 °C and 21 °C, increasing ε from 0 to 0.8 could shorten the melting time by 87.3 %–89.73 %.

Geochemistry and volatile contents of olivine-hosted melt inclusions from Mt. Etna tholeiitic and alkaline magmatism

The analysis of olivine-hosted melt inclusions (MIs) from the whole sub-alkaline and alkaline magmatic suites of Mt. Etna provides fundamental information about the composition of undifferentiated magmas and their pristine volatile content. Olivine crystals (Fo88-66) were selected for Secondary Ion Mass Spectrometry (SIMS) analysis of volatile species (H2O, CO2, F, Cl and S) contained in their host MIs, after preliminary high-pressure/high-temperature re-homogenization, which allowed to reduce the developing of cracks in the host olivine and diffusion-driven outgassing of volatiles from the melt inclusions. This permitted to explore the compositional variability of volatiles of undifferentiated melts and the degassing behavior through the feeding system. The studied MIs show significant major elements compositional heterogeneities (44.57–52.37 wt% SiO2; 3.60–7.51 wt% Na2O + K2O). Fractionation modelling was performed with Rhyolite-MELTs under variable fO2 regimes (∆FMQ + 1.5 to + 3), starting from the less evolved MIs compositions and ultimately reproducing most of the observed compositional trends. Mantle melting modelling was used to replicate the observed MIs composition, starting from a spinel-lherzolitic source, accounting for the alkalinity and Fe content of reproduced melts by varying the eutectic contribution of Amph/Phlog and Opx/Cpx respectively. Although most of the studied MIs were degassed in an open-conduit regime, the observed range of volatile concentration in MIs (2.42–6.14 wt% H2O; 308–8474 ppm CO2; 132–697 ppm F; 221–1766 ppm Cl and 16–1992 ppm S) is correlated with a slight decrease in the molar H2O/(H2O + CO2) ratio from early tholeiites to the recent 2015 alkaline products. This observation allows to estimate a minimum 12,250 ppm CO2 and a maximum of 6.14 wt% H2O in primary melts of the current activity.

Hydrous veined mantle lithosphere and implications for the source of Zealandia intraplate magmas

Although amphibole has long been predicted to be a major component in the mantle source of intraplate volcanic rocks in New Zealand, the physical evidence for this phase, despite inspection of hundreds of peridotite mantle xenoliths from across the country, is limited to a handful of samples in which it is mostly a sparse component. Here, we present a suite of ultra-refractory peridotite xenoliths in an ultramafic lamprophyre from the intraplate Alpine Dike Swarm, New Zealand, that contain abundant MARID-like veins of mica (phlogopite), amphibole (pargasite) and clinopyroxene, with minor to trace rutile, ilmenite, carbonate and apatite. A key feature of inspecting these formerly refractory peridotites (olivine Mg# commonly >92) is that the chemistry of the precipitated metasomatic agent is less diluted than in cases where an invading melt reacts with fertile lithosphere. The bulk compositions of the precipitated veins vary between sub-alkaline basalt and alkaline basanite, with the peridotite wallrock hosting the basanite veins commonly enriched in Fe ± K, Ti and Al. Amphibole in all veins has high Nb, and the 24 Ma age-corrected 87Sr/86Sr values for diopside and amphibole (0.7027 to 0.7031) are indicative of derivation from a depleted mantle free of crustal material, and thus not related to subduction and arc magmatism. The Sr isotope ratios also overlap with the composition of many primitive intraplate magmas across Zealandia. Melt modelling indicates that partial melting of the veins could generate magmas with geochemical aspects of the known intraplate rocks. These rare veined peridotite occurrences therefore confirm that the Zealandia mantle lithosphere contains fusible zones that, if melted, could have played an important role in the source of intraplate basaltic magma.

A Method for Predicting the Melting Temperature of Ionic Compounds.

Predicting the melting temperature of materials has always been a topic of great concern. This article proposes an alternative model for determining the melting temperature of materials based on the main idea of the Lindemann melting criterion combined with the first-principles calculations of density functional theory. To verify the accuracy of the melting model, this article selected typical ionic crystals of MgO and 10 alkali metal halides as the validation objects. The calculation results indicate that the melting temperature of the MgO crystals and I-VII compounds is in good agreement with the experimental results.

Melting and removing wax deposition by thermal washing in oil well

Wax precipitation has proven to be a serious problem when extracting the crude oil from current oilfields. Thermal washing is one of the common methods to remove wax deposition in oil wells. Mastering the melting process and the melting time of the wax layer in thermal washing is essential to optimize operating parameters and further improve the efficiency of thermal washing. In this paper, the scouring model and the melting model are carried out to simulate wax melting behaviour during the thermal washing process in a vertical oil well. Furthermore, with the melting model, the effects of five factors on the melting time have been studied. The results reveal that the melting time is mainly influenced by the thickness of the wax layer and the water flow rate, while the initial temperature of the wax layer, water temperature and inner wall temperature of tubing these three temperatures have a relatively slight influence on the melting time. Finally, with the numerical simulation results, a correlation is developed to predict wax melting time and verified with thermal washing time of the Cha well. It indicates that the melting model is applicable for most of the waxing section, while the scouring model is only applicable when the water initially reaches the bottom of the waxing section, so the melting model is more practical for thermal washing in the oil well.

Plagioclase‐Saturated Melt Hygrothermobarometry and Plagioclase‐Melt Equilibria Using Machine Learning

AbstractCompositions of plagioclase‐melt pairs are commonly used to constrain temperatures (T), dissolved water contents (H2O) and pressures (P) of pre‐eruptive magma storage and transport. However, previous plagioclase‐based thermometers, hygrometers, and barometers can have significant errors, leading to imprecise reconstructions of conditions during plagioclase growth. Here, we explore whether we can refine existing plagioclase‐based hygrothermobarometers with either plagioclase‐melt or melt‐only chemistry (±T/H2O), calibrated using random forest machine learning on experimental petrology data (n = 1,152). We find that both the plagioclase‐melt and melt‐only models return similar cross‐validation root‐mean‐square errors (RMSEs), as the melt holds most of the P‐T‐H2O information rather than the plagioclase. T/H2O‐dependent melt models have test set RMSEs of 25°C, 0.70 wt.% and 76 MPa for temperature, H2O content and pressure, respectively, while T/H2O‐independent models have RMSEs of 38°C, 0.97 wt.% and 91 MPa. The melt thermometer and hygrometer are applicable to a wide range of plagioclase‐bearing melts at temperatures between 664 and 1355°C, and with H2O concentrations up to 11.2 wt.%, while the melt barometer is suitable for pressures of ≤500 MPa. An updated plagioclase‐melt equilibrium model has also been calibrated, allowing the equilibrium anorthite content to be predicted with an error of 5.8 mol%. The new P‐T‐H2O‐An models were applied to matrix glasses and melt inclusions from the 1980 Mount St Helens (USA) and 2014–2015 Holuhraun (Iceland) eruptions, corroborating previous independent estimates and observations. Models are available at https://github.com/kyra‐cutler/Plag‐saturated‐melt‐P‐T‐H2O‐An, enabling assessment of plagioclase‐melt equilibrium and characterization of last‐equilibrated P‐T‐H2O conditions of plagioclase‐saturated magmas.

Discrete element analysis of heating transfer characteristics of airport pavements by using electro thermal method for snow melting and deicing

This study presents a discrete element investigation on the internal temperature change characteristic and heat transfer efficiency in airport concrete pavement by using the carbon fiber electrothermal method for snow melting and deicing. A discrete element model for snow melting and deicing of airport concrete pavement by using the carbon fiber electrothermal method was generated. The temperature evolution on the surface of the pavement was captured and compared with the indoor experimental results. The numerical simulation results were in good agreement with the experimental results, which verified the applicability of the numerical model. On this basis, the effects of the heating temperature and heating paths on the internal heat conduction and temperature field distribution were investigated. The results showed that the temperature of the pavement surface and the temperature rise gradient are linearly related to the temperature of the carbon fiber heating wire. The initial heating time has little influence on the temperature rise path of the road surface layer after stopping heating and reheating. The temperature of the road surface layer rises slowly after the heating is stopped, and then decreases linearly at a rate of 0.4 °C/h not corresponding to the initial heating time.

The origin of Calabi-Yau crystals in BPS states counting

We study the counting problem of BPS D-branes wrapping holomorphic cycles of a general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured Witten index for the supersymmetric quiver quantum mechanics on the worldvolume of the D-branes, and find that BPS degeneracies are described by a statistical mechanical model of crystal melting. For Calabi-Yau threefolds, we reproduce the crystal melting models long known in the literature. For Calabi-Yau fourfolds, however, we find that the crystal does not contain the full information for the BPS degeneracy and we need to explicitly evaluate non-trivial weights assigned to the crystal configurations. Our discussions treat Calabi-Yau threefolds and fourfolds on equal footing, and include discussions on elliptic and rational generalizations of the BPS states counting, connections to the mathematical definition of generalized Donaldson-Thomas invariants, examples of wall crossings, and of trialities in quiver gauge theories.

Numerical investigation of heat transfer in wire and tube-based phase change material heat exchanger

The utilization of latent heat storage units with their high energy density and isothermal heat transfer behavior can enhance the performance of thermal energy systems. This study aims to investigate the effect of fin placement on the melting time of a wire and tube-based Phase Change Material (PCM) heat exchanger using numerical simulations. The study introduces a new complex geometry for the heat exchanger, and numerical analysis of heat transfer was conducted in Ansys Fluent software using an established solidification and melting model. The numerical results were validated against experimental data, and it was found that the position of the tubes and fins had a significant impact on heat transfer within the PCM. The model was able to predict temperature data with a maximum discrepancy of 3%.

Heterogeneous mantle sources for basaltic rocks of the Nagaland–Manipur Hill Ophiolite (NMHO) complex of North-Eastern India: inferences from source melting models

Heterogeneous mantle sources for basaltic rocks of the Nagaland–Manipur Hill Ophiolite (NMHO) complex of North-Eastern India: inferences from source melting models

Gas effects on horizontal ribbon growth

Three-phase (solid, melt, and gas) and two-phase (solid and melt) models of horizontal ribbon growth were compared to identify the significance of different gas effects. The boundary conditions at the melt–gas and solid–gas interfaces for two-phase simulations were obtained from decoupled simulations of the gas phase. The results showed that the gas shear stress strongly changes the flow and temperature fields and the position of the triple-phase line. Also, the gas pressure distribution determined the vertical position of the triple-phase line. In the absence of growth angle effects, the results of the two-phase model with specified convective heat transfer coefficient, shear stress, and pressure as boundary conditions along the gas phase interface closely matched that of the three-phase model. Even with non-zero growth angle effects, the two-phase model with all the boundary conditions agreed well with three-phase simulation results, despite increased deviations at higher pull speeds. Finally, the results indicated that gas-induced velocities are significant compared to the Marangoni and buoyancy velocities, which could lead to flow instabilities and the variations in solid shape as observed in HRG experiments.

A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting.

Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.

A non‐similar solution to dissipative Eyring‐Powell nanofluid flow over a nonlinear stretching surface with an inclined magnetic field and active/passive nanoparticles flux

AbstractAmongst numerous non‐Newtonian fluid models, Eyring‐Powell fluid is prominent owing to its shear thinning, pseudoplastic, and yield stress unique characteristics. It has varied industrial applications including the modeling of polymer melts, food products, and blood flow. This study discusses the Darcy Forchheimer flow of Eyring‐Powell nanoliquid along a nonlinear stretched surface influenced by an inclined magnetic flux. The mass and heat transmissions are supported by active and passive control of nanoparticles respectively. The unique effect of viscous dissipation is introduced to influence the liquid velocity and temperature. Unlike the majority of the research being published that espouses similar solutions, we adopted the non‐similar analysis of the proposed problem to eradicate the chance of the variable in the parameters. This was a challenging task and was taken as a mathematical art rather than a science. The established Buongiorno model is followed to compute the thermophoretic and Brownian motion effects. The numerical computation of this mathematical system is performed using the bvp4c algorithm. The results are described through graphs and in numerically calculated tabulated values. It is determined that wall drag is stronger when the magnetic field is inclined at an angle of than at . Additionally, it is observed that passive control of nanoparticles results in better rates of heat and mass transmissions, against varied values of the fluid parameter with . The validation of the envisioned model is also a part of this exploration.

Temporal numerical analysis of beeswax PCM melting in a cube geometry subjected to a constant wall temperature condition

The ability of phase change materials (PCM) to store thermal energy has gained wide application area, like battery thermal management, solar water desalination and many other. The melting process of beeswax phase change material within the cube geometry with constant wall temperature (65 °C) boundary condition has been investigated using solidification and melting model. The fluid flow and heat transfer governing equations are solved using second order finite volume scheme. A PRESTO algorithm is applied for pressure-velocity coupling. The convergence criteria of 10−10 have been selected for energy equation, while 10−8 is selected for both momentum and continuity equations. The results like percentage variation along length-height and height-width plane for transient liquid fraction and temperature has been plotted, along with velocity streamlines within the cube geometry. From the obtained results it is concluded that the melting fraction and temperature of beeswax PCM is different in different planes and the major factors which affect the complete melting process is wall temperature, and the geometry. A difference of more than 0.1 °C in temperature has been recorded between mid-length-height and height-width plane while a difference of more than 2% in liquid fraction of PCM is observed. Even the uniformity of temperature and liquid fraction is notably influenced and vary along length, height, and width of cube geometry. Thus, it is concluded that melting process of PCM may affect the ability to store and release the heat energy which further affect the performance parameters of applied physical system.

4d crystal melting, toric Calabi-Yau 4-folds and brane brick models

We introduce a class of 4-dimensional crystal melting models that count the BPS bound state of branes on toric Calabi-Yau 4-folds. The crystalline structure is determined by the brane brick model associated to the Calabi-Yau 4-fold under consideration or, equivalently, its dual periodic quiver. The crystals provide a discretized version of the underlying toric geometries. We introduce various techniques to visualize crystals and their melting configurations, including 3-dimensional slicing and Hasse diagrams. We illustrate the construction with the D0-D8 system on \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{C}}$$\\end{document}4. Finally, we outline how our proposal generalizes to arbitrary toric CY 4-folds and general brane configurations.

Numerical Simulation of the Hydrogen-Based Directly Reduced Iron Melting Process

In the context of carbon reduction and emission reduction, the new process of electric arc furnace (EAF) steelmaking based on direct hydrogen reduction is an important potential method for the green and sustainable development of the steel industry. Within an electric furnace for the hydrogen-based direct reduction of iron, after hydrogen-based directly reduced iron (HDRI) is produced through a shaft furnace, HDRI is melted or smelted in an EAF to form final products such as high-purity iron or high-end special steel. As smelting proceeds in the electric furnace, it is easy for pieces of HDRI to bond to each other and become larger pieces; they may even form an “iceberg”, and this phenomenon may then worsen the smelting working conditions. Therefore, the melting of HDRI is the key to affecting the smelting cycle and energy consumption of EAFs. In this study, based on the basic characteristics of HDRI, we established an HDRI melting model using COMSOL Multiphysics 6.0 and studied the HDRI melting process, utilizing pellets with a radius of 8 mm. The results of our simulation show that the HDRI melting process can be divided into three different stages: generating a solidified steel layer, melting the solidified steel layer, and melting HDRI bodies. Moreover, multiple HDRI processes are prone to bonding in the melting process. Increasing the spacing between pieces of HDRI and increasing the preheating temperature used on the HDRI can effectively reduce the aforementioned bonding phenomenon. When the melting pool temperature is 1873 K, increasing the spacing of HDRI to 10 mm and increasing the initial HDRI temperature to 973 K was shown to effectively reduce or eliminate the bonding phenomenon among pieces of HDRI. In addition, with the increase in the melting pool temperature, the time required for melting within the three stages of the HDRI melting process shortened, and the melting speed was accelerated. With the increase in the temperature used to preheat the HDRI, the duration of the solidified steel layer’s existence was also shortened, but this had no significant impact on the time required for the complete melting of HDRI. This study provides a theoretical basis for the optimization of the HDRI process within EAFs.

Quantification of melt pool dynamics and microstructure during simulated additive manufacturing

The dynamics of laser spot melting and metallic alloy solidification are investigated through synchrotron x-ray radiography, 3D electron backscatter diffraction data, and computational fluid dynamics (CFD) simulations on a model NiMoAl alloy. Solidification velocities are measured from in-situ images to validate a CFD model of the spot melt. TriBeam tomography is used to reconstruct the melt pool in 3D, characterize the microstructure, and validate the CFD model melt pool dimensions. 3D geometrically necessary dislocation (GND) density calculations reveal extensive deformation at the sample surface. GND calculations integrated with the CFD model reveal that the halo of small, equiaxed grains adjacent to the fusion line is a result of recrystallization that occurred in the heat affected zone. By combining in-situ and ex-situ data modalities across a variety of temporal and spatial length scales, the microstructure formation mechanisms and their relationship to melt pool solidification are quantified.

A hybrid smoothed-particle hydrodynamics model of oxide skins on molten aluminum

A computational model of aluminum melting is proposed which captures both the thermal fluid-solid phase transition and the mechanical effects of oxidation. The model hybridizes ideas from smoothed particle hydrodynamics and bonded particle models to simulate both hydrodynamic flows and solid elasticity. Oxidation is represented by dynamically adding and deleting spring-like bonds between surface fluid particles to represent the formation and rupture of the oxide skin. Various complex systems are simulated to demonstrate the adaptability of the method and to illustrate the significant impact of skin properties on material flow. Initial comparison to experiments of a melting aluminum cantilever highlights that the computational model can reproduce key qualitative features of aluminum relocation.

Granite magmatism and mantle filiation

Abstract. Current granite magma generation models essentially reduce to two groups: (1) intra-crustal melting and (2) basaltic origin. A mixed, crustal, and basaltic origin and therefore a mantle filiation has been proposed for most granite magma types. In contrast, strongly peraluminous silicic magmas such as two-mica leucogranites have been classically interpreted as products of pure crustal melting. In this paper, we re-examine this interpretation and the evidence for considering leucogranites as unique among granite types. In the first part, some key aspects of the intra-crustal melting model are reviewed. Classical assumptions are discussed, such as the use of migmatites to infer granite generation processes. Our knowledge of crustal melt production is still incomplete, and fluid-present H2O-undersaturated melting should be considered in addition to mica dehydration melting reactions. The source rock remains essential as a concept despite difficulties in the identification of source lithologies from their geochemical and mineralogical signatures. Incorporating spatial and temporal variability at the source and the possibility of external inputs (fluids, magmas) would represent useful evolutions of the model. Thermal considerations bring strong constraints on the intra-crustal melting model since the absence of mafic magmas reduces possible external heat sources for melting. In the second part, the origin of a strongly peraluminous silicic volcanic suite, the Macusani Volcanics (SE Peru), is detailed. Magmas were generated in a mid-crustal anatectic zone characterized by high temperatures and heat fluxes. Crustal metamorphic rocks (metapelites) were dominant in the source region, although Ba-, Sr- and La-rich calcic plagioclase cores and some biotite and sanidine compositions point to the involvement of a mantle component. The heat necessary for melting was supplied by mafic mainly potassic–ultrapotassic magmas which also partly mixed and hybridized with the crustal melts. The Macusani Volcanics provide an example of a crustal peraluminous silicic suite generated with a contribution from the mantle in the form of mafic magmas intruded in the source region. This, as well as the limitations of the intra-crustal melting model, establishes that a mantle filiation is possible for peraluminous leucogranites as for most other crustal (S-, I- and A-type) peraluminous and metaluminous granites. This stresses the critical importance of the mantle for granite generation and opens the way for unification of granite generation processes.