Mushy Region Research Articles

Evaluation of solidification cracking susceptibility during laser welding in advanced high strength automotive steels

Solidification cracking susceptibility during laser welding was studied experimentally and numerically in advanced high strength steel sheets, namely transformation-induced plasticity (TRIP) and dual phase (DP) steel. Using the same heat input, laser bead-on-plate welding was carried out on single sided clamped specimens at various starting distances from the free edge. It was observed that TRIP steel with high phosphorus is susceptible to cracking while in DP steel with low phosphorus, solidification cracking was not observed. The metallurgical factors affecting the solidification cracking were studied and it was found that solidification morphology, phosphorus segregation at the prior austenite grain boundaries, inclusions, interface growth rate and interdendritic liquid feeding have a prominent effect on the strength of the mushy zone. These results are discussed pertaining to the cracking mechanism. For the same welding parameters, a difference in the weld pool shape was observed in both the steels, which is attributed to the high temperature thermophysical properties. Weld pool shape affects the strain distribution in the mushy region and thus the cracking behaviour. The cracking phenomenon is further described using hot ductility curves.

Combined Deformation and Solidification-Driven Porosity Formation in Aluminum Alloys

In die-casting processes, the high cooling rates and pressures affect the alloy solidification and deformation behavior, and thereby impact the final mechanical properties of cast components. In this study, isothermal semi-solid compression and subsequent cooling of aluminum die-cast alloy specimens were characterized using fast synchrotron tomography. This enabled the investigation and quantification of gas and shrinkage porosity evolution during deformation and solidification. The analysis of the 4D images (3D plus time) revealed two distinct mechanisms by which porosity formed; (i) deformation-induced growth due to the enrichment of local hydrogen content by the advective hydrogen transport, as well as a pressure drop in the dilatant shear bands, and (ii) diffusion-controlled growth during the solidification. The rates of pore growth were quantified throughout the process, and a Gaussian distribution function was found to represent the variation in the pore growth rate in both regimes. Using a one-dimensional diffusion model for hydrogen pore growth, the hydrogen flux required for driving pore growth during these regimes was estimated, providing a new insight into the role of advective transport associated with the deformation in the mushy region.

Analytical considerations of thermal storage and interface evolution of a PCM with/without porous media

PurposePhase change energy storage is an important solution for overcoming human energy crisis. This study aims to present an evaluation for the thermal performances of a phase change material (PCM) and a PCM–metal foam composite. Effects of pore size, pore density, thermal conductivity of solid structure and mushy region on the thermal storage process are examined.Design/methodology/approachIn this paper, temperature, flow field and solid–liquid interface of a PCM with or without porous media were theoretically assessed. The influences of basic parameters on the melting process were analyzed. A PCM thermal storage device with a metal foam composite is designed and a thermodynamic analysis for it is conducted. The optimal PCM temperature and the optimal HTF temperature in the metal foam-enhanced thermal storage device are derived.FindingsThe results show that the solid–liquid interface of pure PCM is a line area and that of the mixture PCM is a mushy area. The natural convection in the melting liquid is intensive for a PCM without porous medium. The porous medium weakens the natural convection and makes the temperature field, flow field and solid–liquid interface distribution more homogeneous. The metal foam can greatly improve the heat storage rate of a PCM.Originality/valueThermal storage rate of a PCM is compared with that of a PCM–metal foam composite. A thermal analysis is performed on the multi-layered parallel-plate thermal storage device with a PCM embedded in a highly conductive porous medium, and an optimal melting temperature is obtained with the exergy optimization. The heat transfer enhancement with metal foams proved to be necessary for the thermal storage application.

A study of heat transfer during cryosurgery of lung cancer.

In this study, a mathematical model describing two-dimensional bio-heat transfer during cryosurgery of lung cancer is developed. The lung tissue is cooled by a cryoprobe by imposing its surface at a constant temperature or a constant heat flux or a constant heat transfer coefficient. The freezing starts and the domain is distributed into three stages namely: unfrozen, mushy and frozen regions. In stage I where the only unfrozen region is formed, our problem is an initial-boundary value problem of the hyperbolic partial differential equation. In stage II where mushy and unfrozen regions are formed, our problem is a moving boundary value problem of parabolic partial differential equations and in stage III where frozen, mushy, and unfrozen regions are formed, our problem is a moving boundary value problem of parabolic partial differential equations. The solution consists of the three-step procedure: (i) transformation of problem in non-dimensional form, (ii) by using finite differences, the problem converted into ordinary matrix differential equation and moving boundary problem of ordinary matrix differential equations, (iii) applying Legendre wavelet Galerkin method the problem is transferred into the generalized system of Sylvester equations which are solved by applying Bartels-Stewart algorithm of generalized inverse. The complete analysis is presented in the non-dimensional form. The consequence of the imposition of boundary conditions on moving layer thickness and temperature distribution are studied in detail. The consequence of Stefan number, Kirchoff number and Biot number on moving layer thickness are also studied in specific.

Hyperspectral and thermal temperature estimation during laser cladding

Although there is no doubt about the tremendous industrial potential of metal additive manufacturing techniques such as laser metal deposition, the technology still has some intrinsic quality challenges to overcome before reaching its industrial maturity. Noncontact in situ monitoring of the temperature evolution of the workpiece could provide the necessary information to implement an automated closed-loop process control system and optimize the manufacturing process, providing a robust solution to these issues. However, measuring absolute temperatures is not self-evident: wavelength-dependent emissivity values vary between solid, liquid, and mushy metallic regions, requiring spectral information and dedicated postprocessing to relate the amount of emitted infrared radiation to the material temperature. This paper compares the temperature estimation results obtained from a visible and near-infrared hyperspectral line camera and a conventional short-wave infrared (SWIR) thermal camera during the laser melting and cladding of a 316L steel sample. Both methods show agreeing results for the temperature distribution inside the melt pool, with the SWIR camera extending the temperature measurements beyond the melt pool boundaries into the solid region.

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.

Numerical investigations of freckles in directionally solidified nickel-based superalloy casting with abrupt contraction in cross section

Abstract Evolution of grain structure and formation of freckle defects were simulated in directionally solidified nickel-based superalloy casting with abrupt contraction in cross-section area. A two-dimensional (2D) Cellular Automaton (CA) – Finite Element (FE) model was presented. The transport of liquid momentum, heat and solute mass at macroscopic scale, the development of grain envelopes at mesoscopic scale and microsegregation were fully coupled. Influences of alloying elements, cooling rate and geometrical shape of casting on freckle formation were studied. CAFE simulations show that through reducing the initial concentration of destabilizing element (W), the formation of freckle along casting edges was suppressed. Elements such as Co, Ti and Ta are not critical elements that affect density inversion in mushy region. Increasing cooling rate apparently decreased the freckling tendency. Without geometric contraction, there was no obvious formation of freckles along casting edges. It was numerically showed that the contraction in cross section introduced the high-permeability path for the upward fluid flow during directional solidification, which enhanced the freckling tendency.

Experiments and simulations on solidification microstructure for Inconel 718 in powder bed fusion electron beam additive manufacturing

Previous research on the powder bed fusion electron beam additive manufacturing of Inconel 718 has established a definite correlation between the processing conditions and the solidification microstructure of components. However, the direct role of physical phenomena such as fluid flow and vaporization on determining the solidification morphology have not been investigated quantitatively. Here we investigate the transient and spatial evolution of the fusion zone geometry, temperature gradients, and solidification growth rates during pulsed electron beam melting of the powder bed with a focus on the role of key physical phenomena. The effect of spot density during pulsing, which relates to the amount of heating of the build area during processing, on the columnar-to-equiaxed transition of the solidification structure was studied both experimentally and theoretically. Predictions and the evaluation of the role of heat transfer and fluid flow were established using existing solidification theories combined with transient, three-dimensional numerical heat transfer and fluid flow modeling. Metallurgical characteristics of the alloy’s solidification are extracted from the transient temperature fields, and microstructure is predicted and validated using optical images and electron backscattered diffraction data from the experimental results. Simulations show that the pure liquid region solidified quickly, creating a large two-phase, mushy region that exists during the majority of solidification. While conductive heat transfer dominates in the mushy region, both the pool geometry and the solidification parameters are affected by convective heat transfer. Finally, increased spot density during processing is shown to increase the time of solidification, lowering temperature gradients and increasing the probability of equiaxed grain formation.

Averaging under Rayleigh–Taylor instability and density mushy region generation

Abstract A stratified liquid with two layers separated by a fast oscillating interface in the case of Rayleigh–Taylor instability is considered. The averaged equations are derived, and it is shown that a mushy region of a certain density appears after averaging. The similarity between this fact and the case of unstable jump decay is discussed.

Solid-liquid phase-change thermal storage and release behaviors in a rectangular cavity under the impacts of mushy region and low gravity

The work aims to address the effects of mushy zone constant (1 × 104 ≤ C ≤ 1 × 108 kg m−3 s−1) and gravitational acceleration (1.635 ≤ g ≤ 9.810 m s−2) on the thermal storage/release behaviors of paraffin wax (phase change material, PCM), by performing numerical investigations in a rectangular cavity with partially thermal active walls. The enthalpy-porosity method is employed to simulate the solid–liquid phase-change process and flow evolution at the PCM interface. The numerical model is validated by the published literature data. It is confirmed that the thermal storage behaviors are significantly influenced by the mushy zone constant and gravitational acceleration. PCM liquid fraction is essentially increased as decreased in mushy zone constant and increased in gravitational acceleration, with maximum discrepancies are reached 88%. However, very limited impacts are conducted on the thermal release process with maximum PCM liquid fraction discrepancy only 2%. Furthermore, the proposed equations regarding how to calculate the value of mushy zone constant are also outlined and commented. Therefore, proper examination and verification for mushy zone constant is very important and necessary before solid–liquid phase-change thermal storage process is accurately simulated by enthalpy-porosity model.

A study of cryosurgery of lung cancer using Modified Legendre wavelet Galerkin method

In this paper, we have developed a new mathematical model describing bio-heat transfer during cryosurgery of lung cancer. The lung tissue cooled by a flat probe whose temperature decreases linearly with time. The freezing process occurs in three stages and the whole region is divided into solid, mushy and liquid region. The heat released in the mushy region is considered as discontinuous heat generation. The model is an initial-boundary value problem of the hyperbolic partial differential equation in stage 1 and moving boundary value problem of parabolic partial differential equations in stage 2 and 3. The method of the solution consists of four-step procedure as transformation of problem in dimensionless form, the problem of hyperbolic partial differential equation converted into ordinary matrix differential equation and the moving boundary problem of parabolic partial differential equations converted into moving boundary problem of ordinary matrix differential equations by using finite differences in space, transferring the problem into the generalized system of Sylvester equations by using Legendre wavelet Galerkin method and the solution of the generalized system of Sylvester equation are solved by using Bartels-Stewart algorithm of generalized inverse. The whole analysis is presented in dimensionless form. The effect of cryoprobe rate on temperature distribution and the effect of Stefan number on moving layer thickness is discussed in detail.

Two zone model for mushy region of solid–liquid phase change based on Lattice Boltzmann method

The solid-liquid phase change technology has been widely used in the efficient use and controllable management of heat in engineering. It is important to reveal the transfer mechanism of phase change interface for the optimization of solid-liquid phase change technology. A composite model of heat transfer and fluid flow in mushy zone is established by using the modified enthalpy method based on the combination of porous medium flow and multiphase flow theory. Lattice Boltzmann Method is used to solve the transient model of multi-field coupling in mushy zone in pore scale. The transfer mechanism in solid-liquid phase change, especially at the solid-liquid interface in mushy zone is focused on in this paper. The numerical results show that the thickness of mushy region is directly related to the phase change temperature radius of the mushy region. A smaller phase change temperature radius of the mushy region leads to a thinner mushy region thickness. The results also indicate that the mushy region constant (C) and demarcation point (rtr) of high-low liquid fraction area, phase change materials and the structure of mushy region have a close relationship with each other. The dimensionless parameters (Pr, Ra, Ste) of phase change process have an obvious influence on the mushy region and the phase change process.

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.

Prediction of Shrinkage Defects in Iron Castings Using a Microporosity Model

A numerical model for prediction of shrinkage defects in iron castings has been developed. The model is based on gas pores evolution during solidification. It describes the evolution of gas concentration using mass conservation, and the change in melt pressure due to solidification contraction using Darcy’s equation, with mixture continuity assumption in the liquid and the mushy zone. Gas pores nucleation has been calculated using the partial pressure of gas obtained from Sievert’s law. The growth of porosity has been estimated using an equation based upon the total melt pressure on the pore, concentration and temperature of the gas. The porosity model was calibrated against literature data for microporosity, and then applied to the prediction of shrinkage defects in a ductile iron casting. Comparison between the model predictions and experimental measurements indicated that the porosity model can be applied not only to the prediction of micro-shrinkage but also to that of macro-shrinkage. Existing shrinkage prediction models based upon thermal models, such as Niyama criterion and the modulus of retained melt in mushy regions cannot predict correctly both micro- and macro-shrinkage.

Experimental, numerical and analytic study of unconstrained melting in a vertical cylinder with a focus on mushy region effects

The enthalpy-porosity method is widely used in solving solid-liquid phase change problems that involve convection in the melt; however the influence of the required mushy zone parameter on the melting process has been largely overlooked. In this paper, further investigation of the mushy zone parameter is presented. The enthalpy-porosity method is the default model in Fluent for melting simulations. A comprehensive discussion of previously reported mushy zone parameter values is presented with a comparison to numerical and experimental results. In this paper, based on experimental validations of melting times, it is found that mushy zone parameters can be optimized based on relevant driving temperature differences. And despite the fact that the model cannot capture bulk solid sinking behaviors, numerical solid sinking behaviors by Fluent are still widely reported in the literature. Explanations and supporting numerical analysis are given for this seeming contradiction. Finally, an analytic solution for unconstrained sinking is developed. With the introduction of a tuning parameter to modify the viscosity of the mushy region in the bottom liquid layer, good agreement between the analytical model and experimental results is achieved. A linear correlation for the tuning parameter based on driving temperature differences is given.

Energy Storage by Melting Commercial Change Phase Materials in Hexagonal-Shaped Heat Exchangers

A two-dimensional melting of a technical-grade phase-change material is modeled. The phase-change material is placed in the annular space formed by an outer regular hexagonal tube and an inner tube. A nonorthogonal boundary fitted coordinate method is implemented on a staggered grid arrangement. The mushy region of the impure phase-change material has been accommodated through the enthalpy-porosity scheme. A set of parametric studies is carried out. Selected results are presented as a function of time for the velocity and temperature fields, the cumulatively stored energy, the total melt fraction, and the average Nusselt number on the inner tube. The oblate-shaped inner tube results in the highest melting rate and stores the maximum energy among the studied units irrespective of the shape and vertical position of the inner tube. Among the three vertical positions of the inner circular tube, when the center of the inner tube is placed at one-third height from the base of the outer tube, it shows the greatest thermal efficiency, and the worst performance is obtained for the upper position of the inner tube at the two-thirds height of the outer tube. With the increase in the Rayleigh number (wall temperature), the amount of energy storage is enhanced.

Production, pathways and budgets of melts in mid-ocean ridges: An enthalpy based thermo-mechanical model

Using an enthalpy based thermo-mechanical model we provide a theoretical evaluation of melt production beneath mid-ocean ridges (MORs), and demonstrate how the melts subsequently develop their pathways to sustain the major ridge processes. Our model employs a Darcy idealization of the two-phase (solid-melt) system, accounting enthalpy (ΔH) as a function of temperature dependent liquid fraction (ϕ). Random thermal perturbations imposed in this model set in local convection that drive melts to flow through porosity controlled pathways with a typical mushroom-like 3D structure. We present across- and along-MOR axis model profiles to show the mode of occurrence of melt-rich zones within mushy regions, connected to deeper sources by single or multiple feeders. The upwelling of melts experiences two synchronous processes: 1) solidification-accretion, and 2) eruption, retaining a large melt fraction in the framework of mantle dynamics. Using a bifurcation analysis we determine the threshold condition for melt eruption, and estimate the potential volumes of eruptible melts (∼3.7 × 106 m3/yr) and sub-crustal solidified masses (∼1–8.8 × 106 m3/yr) on an axis length of 500 km. The solidification process far dominates over the eruption process in the initial phase, but declines rapidly on a time scale (t) of 1 Myr. Consequently, the eruption rate takes over the solidification rate, but attains nearly a steady value as t > 1.5 Myr. We finally present a melt budget, where a maximum of ∼5% of the total upwelling melt volume is available for eruption, whereas ∼19% for deeper level solidification; the rest continue to participate in the sub-crustal processes.

Solidification and Flow of a Binary Alloy Over a Moving Substrate

We study the solidification and flow of a binary alloy over a horizontally moving substrate. A situation in which the solid, liquid and mushy regions are separated by the stationary two-dimensional interfaces is considered. The self-similar solutions of the governing boundary layer equations are obtained, and their parametric dependence is analysed asymptotically. The effect of the boundary layer flow on the physical characteristics is determined. It is found that the horizontal pulling and the resulting flow in the liquid enhance the formation of the mushy region.

Numerical simulation of a finned-tube LHTES system: influence of the mushy zone constant on the phase change behaviour

This work presents a numerical investigation on latent heat thermal energy storage (LHTES) systems during the phase change process. The numerical analysis, based on the apparent heat capacity formulation, was carried out through a two-dimensional axisymmetric numerical model developed by means of the COMSOL Multiphysics software. A thermal energy storage system based on the configuration of a double tube heat exchanger with finned surfaces was used as an experimental test case and the commercial paraffin RT35 was selected as phase change material (PCM). The influence of the heat transfer by convection, in particular the influence of the term describing the mushy zone in the momentum equation, was investigated during the whole charge and discharge processes. Three different values of the constant Amush, equals to 104, 106 and 108 were selected as well as two different values of the HTF volumetric flow rate were adopted in order to reproduce both laminar and turbulent flow regimes. The results are reported in terms of temperature, melting fraction and phases evolution during the whole melting and solidification processes, and compared to previous experimental tests carried out in the laboratories of the University of Lleida, Spain. A good agreement with the experimental results was obtained showing that the mushy zone constant has a significant influence on the interface shape and motion. The results show that large values of Amush determine an increase of the mushy region reducing the natural convection effects during the charge phase. Thus, the proper evaluation of the mushy zone constant allows providing a deeper understanding of the phase change behaviour, resulting in an important parameter for accurate modelling of LHTES systems.

Industrial Direct Chill Slab Caster of Tin Bronze (C903) Using a Porous Filter in the Hot-Top

A 3D computational fluid dynamics (CFD) modeling study has been carried out for the tin bronze (C903) slab of industrial size in a vertical direct chill caster. The melt is delivered from the top across the entire cross section of the caster. An insulated hot-top is considered above the 80-mm mold to control the melt level in the mold. A porous filter is considered in the hot-top region of the mold to arrest the incoming inclusions and homogenize the flow into the mold. The melt flow through the porous filter is modeled on the basis of the Brinkmann–Forchheimer-extended non-Darcy model. Results are obtained for four casting speeds varying from 40 to 100 mm/min. The metal–mold contact region, as well as the convective heat transfer coefficient at the mold wall, is also varied. In addition to the above, the Darcy number for the porous media is also changed. All parametric studies are performed for a fixed inlet melt superheat of 62 °C. The results are presented pictorially in the form of temperature and velocity fields. The sump depth, mushy region thickness, solid shell thickness (ST) at the exit of the mold, and axial temperature profiles are also presented and correlated with the casting speed through regression analysis.