Mathematical modeling of bulk and directional crystallization with the moving phase transition layer

This paper is devoted to the mathematical modeling of a combined effect of directional and bulk crystallization in a phase transition layer with allowance for nucleation and evolution of newly born particles. We consider two models with and without fluctuations in crystal growth velocities, which are analytically solved using the saddle-point technique. The particle-size distribution function, solid-phase fraction in a supercooled two-phase layer, its thickness and permeability, solidification velocity, and desupercooling kinetics are defined. This solution enables us to characterize the mushy layer composition. We show that the region adjacent to the liquid phase is almost free of crystals and has a constant temperature gradient. Crystals undergo intense growth leading to fast mushy layer desupercooling in the middle of a two-phase region. The mushy region adjacent to the solid material is filled with the growing solid phase structures and is almost desupercooled.

Convection in a mushy layer along a vertical heated wall

Motivated by the mushy zones of sea ice, volcanoes and icy moons of the outer solar system, we perform a theoretical and numerical study of boundary-layer convection along a vertical heated wall in a bounded ideal mushy region. The mush is comprised of a porous and reactive binary alloy with a mixture of saline liquid in a solid matrix, and is studied in the near-eutectic approximation. Here, we demonstrate the existence of four regions and study their behaviour asymptotically. Starting from the bottom of the wall, the four regions are (i) an isotropic corner region; (ii) a buoyancy dominated vertical boundary layer; (iii) an isotropic connection region; and (iv) a horizontal boundary layer at the top boundary with strong gradients of pressure and buoyancy. Scalings from numerical simulations are consistent with the theoretical predictions. Close to the heated wall, the convection in the mushy layer is similar to a rising buoyant plume abruptly stopped at the top, leading to increased pressure and temperature in the upper region, whose impact is discussed as an efficient melting mechanism.

Density and thermal expansion of the nickel-based superalloy INCONEL 625 in the solid and liquid states

Density and thermal expansion of the nickel-based superalloy INCONEL 625 were measured in the temperature range 150 °C to 1400 °C using pushrod and piston dilatometry. Commercial pushrod-dilatometers were used for the measurements. The specimens are cooled and heated slowly at controlled rates in a furnace; the expansion is transferred by a long thin rod to displacement sensors. In the high temperature range an alumina tubular body with two alumina pistons of just sufficient clearance was used to contain the specimen in the mushy region and in the liquid state The investigated material was primary heat treated at 930 °C for 1 hour. As INCONEL 625 is an age-hardening alloy, the thermophysical properties including density at elevated temperature depend slightly on heat treatment conditions. Therefore, different measurement runs with a variation of the maximum temperature in the solid state (from room temperature to 1000 °C, 1100 °C and 1250 °C) were performed to cover different heat treatments (product grades) of INCONEL 625. Due to the lack of density and thermal expansion data of INCONEL 625 in the solid and liquid states in the literature, the measured density is compared to published density data of INCONEL 718 and INCONEL 738. A detailed uncertainty analysis of the measured data in the solid and liquid state of the alloy is provided.

A Nonlinear Dynamic Switched-Mode Model of Twin-Roll Steel Strip Casting

During twin-roll steel strip casting, molten steel is poured onto the surface of two casting rolls where it solidifies to form a steel strip. The solidification process introduces a two-phase region of steel known as mushy steel which has a significant effect on the resulting quality of the manufactured steel strip. Therefore, an accurate model of the growth of mushy steel within the steel pool is imperative for ultimately improving strip quality. In this paper, we derive a reduced-order model of the twin-roll casting process that captures the dynamics of the mushy region of the steel pool and describes the effect that the casting roll speed and gap distance have on the solidification dynamics. We propose a switched-mode description that leverages a lumped parameter moving boundary approach, coupled with a thermal resistance network analogy, to model both the steel pool and roll dynamics. The integration of these models and simulation of the combined model are nontrivial and discussed in detail. The proposed reduced-order model accurately describes the dominant dynamics of the process while using approximately one-tenth of the number of states used in previously published models.

Macroscopic models for calcium carbonate corrosion due to sulfation. Variation of diffusion and volume expansion

The subject of the present paper is the derivation and analysis of mathematical models for the formation of a mushy region during calcium carbonate corrosion. More specifically there is emphasis on the variation of the overall diffusion resulting from the changing shape of a single pore due to corrosion process and on the resulting volume expansion of the material as the outcome of the transformation of calcium carbonate to gypsum. These models are derived by averaging, with the use of the multiple scales method applied on microscopic moving-boundary problems. The latter problems describe the transformation of calcium carbonate into gypsum in the microscopic scale. The derived macroscopic models are solved numerically with the use of an implicit in time, finite element method. The results of the simulations for various microstructure geometries in the micro-scale and a discussion are also presented.