Mushy Region Research Articles

Artificial intelligence based experimental investigation of underwater fiber laser transmission process during micro-channelling operation on PMMA

Industries that engage in laser-based material processing are increasingly turning to fiber lasers as one of the most effective laser systems available. Using a pulsed fiber laser system, an experimental investigation of underwater laser micro-channelling on hard to machine thick PMMA has been conducted in this research work. Submerged laser transmission cutting which is also known as underwater laser induced backside machining helps to generate clean kerf edge without presence of mushy region, which is very common during laser machining of thick PMMA with wavelength of near infrared region. Submerged conditions are used here for laser transmission micromachining in order to reduce adverse thermal effects and microcracking or charring inside the material. Pulse frequency, working power, and cutting speed have been selected as the input parameters. As machining responses, the depth of the micro-channel, the width of the kerf, and the width of the heat affected zone (HAZ) have been considered. To find the ideal parametric condition for simultaneously achieving numerous goals, Response Surface Methodology (RSM) and AI-based Teaching Learning-Based Optimisation (TLBO) have been used. The TLBO technique determined that the optimal laser machining settings are a power setting of 13.98 %, a pulse frequency of 50 kHz, and a cutting speed of 0.20 mm/sec. These parameters result in a minimum HAZ width of 4.1874 µm, a minimum kerf width of 22.3698 µm, and a maximum depth of cut of 37.1478 µm. Underwater laser processing reduces heat affected zone and redeposition surrounding micro-channels, creating a cleaner, finer structure.

Numerical modelling of continuous casting of round billets with turbulence in the melt

The present work aims to solve the continuous casting benchmark problem in axisymmetry with turbulence in the melt by the meshless method. The physical model of the liquid-solid system that involves mass, momentum and energy conservation is formulated in the mixture continuum approximation. The melt is assumed Newtonian and incompressible. A k-epsilon Reynolds averaged Navier-Stokes turbulence model is implemented with Abe-Kondoh-Nagano closures. The mushy region is modelled as a Darcy porous media with the Kozeny-Carman permeability model. The solution of partial differential equations is implemented locally using collocation with radial basis functions and explicit time-stepping. The velocity pressure coupling is performed using the fractional step method. The validation of the model is assessed by comparing its outcomes with the results of the finite volume method. A sensitivity study of the varying casting speed and temperature on the velocity, temperature, and solid fraction fields is shown.

A computational study of binary eutectic system with convection under volumetric freezing: A Moving Boundary Problem

A reduction in the operating time during the solidification of an eutectic alloy is one of the prime demands in front of the investigators. The classical theory of solidification was not able to offer rapid solidification of an alloy due to not account the structural property of the material. To account convection and external heat sink effect, an external volumetric heat sink is considered and it depends on the distance and time. The thermal conductivity, density, and specific heat of the mushy zone are assumed to be the linear combination of solid and liquid regions properties with a solid fraction distribution. The mathematical model accounts for the solid fraction distribution, which has a linear relationship with the temperature of the mushy zone. The analytical solution of the problem has been determined via similarity transformation. To explore the current study, numerical data of the Copper-Aluminum alloy with 5% Copper is presented. It has been found that with a volumetric heat sink, the rate of solidification becomes faster than usual. Further, the rate of heat removal from the surface accelerates. Convection enhances the rate of freezing of the eutectic alloy. The temperature of the mushy region is going up for the increasing value of the solid fraction in mushy zone, which is lying in [0,1] and when we increase the strength of volumetric heat, then the temperature profile decreases and, the first-interface and second-interface increase gradually in the whole medium. We compared the current result with Tien and Geiger’s result, and it is found in good compliance. It is expected that the current study will improve the fundamental understanding of the solidification of an eutectic alloy and reduce the time for freezing, which is useful to design industrial freezing devices for alloys.

Solidification cracking susceptibility and carbide evolution behavior in ERNiMo-2 weld metal: Effect and mechanism of Si content

ERNiMo-2 wire is the matching welding filler metal for the GH3535 alloy, which is prone to occur solidification cracking during welding. Optimizing the composition of ERNiMo-2 wire is an effective way to reduce the welding solidification cracking susceptibility (WSCS) and improve the performance of GH3535 alloy welded joint. In this study, the WSCS of ERNiMo-2 wires with different Si content was evaluated by the trans-varestraint test, and the mechanism of Si affecting the weldability of ERNiMo-2 wire was revealed. The results showed that the solidification cracking temperature range (SCTR) of Si1-Si4 wires with Si content increasing is 102 °C, 123.2 °C, 119.1 °C and 116.3 °C, respectively. The existence of eutectic M2C and M6C in the form of liquid film at the end of solidification leads to partial wetting of the grain boundary, which reduces the binding force of the grain boundary and promotes crack initiation. Low solidification shrinkage, thermal shrinkage, solidification temperature range and a small amount of eutectic liquid in the mushy region make the Si1 wire have the best resistance to solidification cracking. The aforementioned factors increase with Si content, then resulting in the increase of WSCS of Si2. However, the amount and fluidity of eutectic liquid in weld metal increase when the Si content increases to Si3 and Si4, which leads to the occurrence of eutectic backfilling and decrease in WSCS of ERNiMo-2 wire.

Investigation of Solidification Heat Transfer in Slab Continuous Casting Process Based on Different Roll Contact Calculation Methods.

The heat transfer of a slab is significantly influenced by roll contact during the continuous casting process. The influence of roll contact calculation methods on the predicted heat transfer results has not been previously investigated. In this work, the non-uniform solidification of the wide-thick slab was studied with a 2D heat transfer model using real roll contact method (R. method) and equivalent roll contact method (E. method). The predicted slab surface temperature and shell thickness were verified with the measured results of the infrared camera and nail shooting experiments, respectively. Then, the predicted heat transfer results (including the slab surface temperature, mushy region length, and solidification end position) for the wide-thick slab with different thicknesses and different casting speeds were calculated using the E. method and R. method, and the influence of these two roll contact methods on the predicted heat transfer results was discussed for the first time. The results show that both these two roll contact methods could be applied to accurately predict the slab surface temperature without considering the transient temperature dips in the roll-slab contact regions. However, the deviation of the predicted mushy region length and solidification end position using the E. method are obvious. Compared with the R. method, the predicted mushy region length obtained using the E. method is larger and the solidification end obviously subsequently moves along the casting direction.

Understanding of macro-segregation in direct-chill cast 2024 alloy with intensive melt shearing based on the evolution of microstructure and temperature field

The influence of intensive melt shearing (IMS) on macro-segregation has been systematically investigated. Experimental results show that the negative centerline segregation is effectively suppressed when the IMS is applied. To reveal the mechanism of IMS on macro-segregation, a quantitative study on the evolution of the slurry region, mushy region, solidification interface, morphology, and concentration of microstructure was carried out. It was confirmed that the IMS parameters determine the dominant mechanism affecting centerline segregation by controlling its action region. When IMS is applied above the liquidus, the fine dendritic structure not only has higher solute content, but also effectively limits the penetration depth of the liquid melt. Moreover, the velocity of the shrinkage flow in the horizontal direction decreases due to the flattening of the solidification interface. At this condition, the above factors play a more dominant role in macro-segregation than the increase of the mushy region thickness. When the action region of IMS changes to the slurry region, the solidification interface profile transforms from a “V” shape to a “VVV” shape. In this case, the influence of the magnitude and direction of the shrinkage flow on macro-segregation is balanced by the near-spherical structure (solute-poor), the increase of permeability, and the thickness of the mushy region. A physical model has been proposed to explain the IMS parameters on macro-segregation.

The role of the phase-change material properties, porosity constant, and their combination for melting problems using the enthalpy-porosity scheme

This study investigates the effects of consistently altering the PCM thermophysical properties, the porosity constant, and their combination on the accuracy of melting models. To the best of the authors’ knowledge, this is the first systematic evaluation of this coupled effect, which challenges a common literature practice: to validate the model and use it with another PCM or in a completely different scenario. To this end, a mathematical model is formulated and numerically solved with Ansys® Fluent, being validated with two experimental datasets, comprising distinct geometries and PCM properties. Initially, the discussion centers on the alteration of the porosity constant, revealing its sensitivity in both isothermal and non-isothermal PCMs, with a more pronounced influence in materials exhibiting a mushy region. Subsequently, the effect of altering the parameters included in the Boussinesq approximation was assessed, being shown that a proper selection of the coefficient of thermal expansion is more critical than that of density, altering the liquid fraction in 7.5% and 0.5%, respectively. The phase-change temperature also influenced the results, with a 6.9% higher deviation when switching from the liquidus to the average solidus–liquidus temperature. Furthermore, it was evidenced that, by holding the porosity constant of validation in another geometry, deviations as high as 38.0% could be achieved, whereas this error could be reduced to 5.7% with a proper adjustment. This discrepancy may be even greater if the PCM is altered, leading to unclear results. Lastly, the study provides valuable insight suggesting that, as natural convection intensifies, reducing the porosity constant can mitigate errors. These findings hold practical significance for models developed using the enthalpy-porosity scheme, emphasizing the importance of careful consideration when extending the model applicability beyond the validation conditions.

Directional Crystallization in the Presence of a Mushy Layer with Applications to the Earth’s Inner Core Boundary

We formulate the mathematical model of directional crystallization of a binary melt with a mushy layer (region) between purely solid and liquid phases. This model is complicated by melt convection and pressure-dependent phase transition temperature. Approximate analytical solutions to this nonlinear moving-boundary problem are constructed. Namely, the concentration of impurity, fraction of solid phase, mushy region thickness, average fluid velocity, primary interdendritic spacing, mean radius of a chimney, and a characteristic distance between chimneys in a mushy region are found. Using this analytical solution, we describe the mushy region structure near the inner core boundary of the Earth, which is consistent with computer simulations and estimates existing in recent literature. A scheme illustrating the mushy region arrangement with chimneys at the inner core boundary of the Earth is presented. This arrangement based on the developed theory represents the novelty and importance of our study.

Numerical investigation of the effect of thermal expansion coefficient and mushy zone constant on modelling of the phase change process to provide reliable selection criteria of modelling parameters

Phase change materials (PCMs) have been involved in many critical applications due to their ability to store thermal energy and stabilize the temperature. The accuracy of PCMs numerical modelling is affected by the software input assumptions including the thermal expansion coefficient and the mushy zone parameter. The thermal expansion coefficient is used to calculate the density value, to be applied in the modelling equations, but volume expansion is generally not considered by PCM modelling softwares. Due to this fact, the assumed value for the thermal expansion coefficient has to be selected properly, before conducting numerical tests. Another influential input is the mushy zone constant that has a significant effect on the output results, and it has to be selected from a wide range of values between 103 and 1010.In this study a numerical investigation for the influence of both parameters was conducted to provide valid selection criteria. It was found that changing the expansion coefficient controlled the melting process time without affecting the melting profiles, where increasing the expansion coefficient accelerated the melting process, reducing the melting time and vice versa. The melting interface profiles were found directly related to the mushy zone parameter. Increasing the mushy zone parameter value decreased heat transfer rate through the mushy region, which significantly changed the melting profiles. These tests were repeated using different orientations to confirm these findings. Finally, reliable selection criteria were introduced to select the proper values for numerical modelling of phase change process. This selection process was tested using Lauric acid material at different orientations.

Simulation of liquid & solid metal regions in a continuous casting process using COMSOL Multiphysics

Continuous casting (CC) is the primary method in the production of metal billets, blooms, or slabs. Modeling & simulation of a CC is a complex phenomenon involving many physics. In this present study, laminar flow and heat transfer, physics were taken into count. And considering the phase change volume fraction during the solidification process. A steady-state model of the Enthalpy technique was used which treats the mushy region liquid fraction of metal in the mushy region has been traced to find the solidified shell thickness. A steady-state 2D – Axisymmetric model is taken into count. Three case studies are studied for cast velocities of 8, 16, and 32 mm/s with varying two combinational sets of cooling on primary & secondary zones. i.e. water plus air & water plus water. The heat transfer, solidification, and phase volume fractions length were investigated.

Directional crystallization with a mushy region. Part 1: linear analysis of dynamic stability

Directional crystallization with a mushy region. Part 1: linear analysis of dynamic stability

Directional crystallization with a mushy region. Part 2: nonlinear analysis of dynamic stability

Directional crystallization with a mushy region. Part 2: nonlinear analysis of dynamic stability

A general non-Fourier Stefan problem formulation that accounts for memory effects

The Stefan problem is the classical model of a melting phase change. In heterogeneous systems, such phase changes can exhibit non-Fourier (anomalous) behaviors, where the advance of the melt interface does not follow the expected time scaling. These situations can be modeled by replacing the derivatives, in the governing partial differential equations, with fractional order derivatives. In particular, replacing the time derivatives leads to non-Fourier models that account for memory effects in the system. In this work, by using appropriate time convolution integrals, a general thermodynamic balance statement for melting phase problems, explicitly accounting for memory effects, is developed. From this balance, a general model formulation applicable to problems involving melting over a temperature range (i.e., a mushy region) is derived. A key component in this model is the representation of memory effects through the use of fractional derivative based constitutive models of the enthalpy and heat flux. On shrinking the mushy region to a single isotherm, a general sharp interface melting model is obtained. Here, in contrast to the classic Stefan problem, the fractional derivatives induce a natural regularization, such that the constitutive models for enthalpy and heat flux are continuous at the melt interface; a result confirmed through numerical simulation. To further support the theoretical findings, a physical example of a non-Fourier Stefan problem is presented. Overall the development and results in this paper underscore the importance of explicitly relating the development of fractional calculus models to the appropriate thermodynamic balance statements.

Simulation of macrosegregation in continuous casting of steel based on large-eddy simulation turbulence model and meshless solution procedure

The formation of macrosegregation pattern in steel is explored for the continuous casting process. The related solidification problem is described by incompressible turbulent fluid flow, governed by mass, momentum, energy, and species conservation equations. The solid-liquid system is designed in a mixture continuum model formulation, and the mushy region is approximated with the Darcy model. The lever rule describes the formation of microsegregation of carbon. Turbulence is modelled with a large-eddy simulation approach implemented with the Smagorinsky model and van Driest correction. The synthetic isotropic fluctuations of the inlet velocity are generated by the von Karman Pao spectrum. The solution of partial differential equations is implemented locally by using collocation with radial basis functions for spatial discretization and the explicit Euler method for time discretization. The two-dimensional large eddy simulation model solutions are compared to the previously calculated examples obtained with the low-Re k − ε turbulence model.

Thermal Performance Assessment for an Active Latent Heat Storage Tank by Using Various Finned-Coil Heat Exchangers

Paraffin-based latent heat storage has a higher thermal capacity than sensible heat storage. Despite that, the actual implementation of paraffin as an active latent heat storage (ALHS) system is limited due to low charging and discharging rate with unequal temperature distribution as the impact of mushy region formation. The present study evaluates the finned-coil heat exchanger for the ALHS tank to overcome the related problems. Three finned-coil configurations are tested experimentally: straight-fin, branched-fin and height-fin. The evaluation uses the ALHS arrangement to assess each configuration's charging/discharging rate. The branched fin provides an equal thermal distribution, promoting a higher final temperature of 112.3°C. It also achieves the highest power rate of 250.5 Watts. The height-fin minimizes the effect of void formation, which maintains a sufficient heat transfer rate during the discharging. However, the average power rate for each model is relatively low. The finding indicates that it is essential to provide adequate heat transfer for the center part of the tank, including adding a branched fin along with coil turn to provide a better heat transfer rate. It boosts the charging/discharging rate, making the system's response time desirable to achieve effective power during the operation.

Simulation of Phase Change Material Absorbers for Passive Cooling of Solar Systems

One of the main challenges that face the reliable use of photovoltaic solar systems in hot arid regions is the prevailing high temperatures during the day. To overcome this issue, Phase Change Materials (PCM) are used for passive cooling providing different options to attain sufficient thermal management solutions for different applications. Passive cooling can be achieved by adjusting a heat sink to the solar PV module. This can be realized by attaching a PCM layer or sensible heat storage to the backside of PV panels. Few studies have reported on simplified modeling and numerical procedures using the apparent heat capacity formulation and volume averaging technique as a robust approach to solving such sophisticated problems with minimal computational efforts, high accuracy, and in a short period of time. However, there is still a need to bridge the large-scale gap between the macroscale within the PCM layer, with a moving melting front, and the length scale of PV modules. Hence, this work focuses on modeling and simulating PCM-Matrix Absorbers (PCM-MA) that consist of fibrous aluminum cellular structure filled with PCM for passive thermal management of PV panels using apparent heat capacity formulation and homogenization based on volume averaging technique. COMSOL Multiphysics FEM software was used for the numerical simulation of the phase change problem by using a Smoothed Heaviside step function to overcome the singularity of PCM challenge that arises with sharp melting temperatures. To validate the proposed model, it has been compared with a benchmark analytical solution for an ice melting problem, i.e., the Stefan problem, in a semi-finite slab, i.e., Neumann’s solution under the same assumptions and boundary conditions. The specific characteristics of phase change and evolution of melting front with time, heat capacity change with the temperature at different times, and with locations along the slab height are presented. As the phase change is modeled to take place over a mushy region, i.e., a narrow temperature interval rather than a sharp melting point, the results show a good coincidence of the heat capacity profile and its peak at different times and locations. The validated model can be used for the optimization of PCM-MA for any specific geographical location and other applications such as the passive cooling of buildings with PCM integrated with the outer envelope. To this end, the results of the simulation in this work are shown to be in agreement with those obtained from the analytical solution.

Prediction of permeability in mushy zone of Al-4.5 %Mg alloy based on CA-LBM model

Permeability is a key parameter in hot tearing prediction, and the solidification microstructure of alloys has an important influence on permeability prediction. The present paper builds a cellular automata–lattice Boltzmann method (CA-LBM) model to simulate the grain growth and liquid flow of semi-solid binary aluminum alloys. The CA model was used to simulate the microstructure of the mushy region, including the growth of dendrites and the overlap between the dendrite arms, and the LBM model was used to observe the liquid phase flow in the mushy zone. The model takes into account the complex inter-dendritic flow, including the liquid flow between the dendrite arms. The paper compared the permeability results of the current model with the Carman–Kozeny equation for two limiting cases of interfacial area concentration Sv (the dendrite structure with Sv and the globular structure with Sv) and investigated the effect of different cooling rates on permeability. Deviation from the Carman–Kozeny behavior was observed with a transition in microstructure, i.e., when the domain contained a mixture of dendritic and globular structures or when fluid flow occurred simultaneously in the intra-dendritic and extra-dendritic regions. From the analysis of the permeability results of the mushy zone under different cooling rates, the higher the cooling rate, the lower the permeability. The permeability is not only related to the solid volume fraction but also to the morphology and size of grains.

A study of dual phage lag model of heat transfer for solidification of binary eutectic alloy

In this paper, we developed a generalized non-Fourier model of energy transfer for solidification of a binary eutectic system (Al-Cu alloy). The mathematical model is divided into three stages: stage I (liquid region), II (liquid and mushy region), and III (liquid, mushy and solid region). The analysis of the model has been done in dimensionless form. This model is a boundary value problem of the system of second-order hyperbolic partial differential equations for Stage I, the moving boundary problem of the System of second-order hyperbolic partial differential equations for Stage II and III. For the solution, we applied Laplace transform technique in Stage I and Legendre wavelet spectral Galerkin method in Stage II and III. The effect of unit-less parameters: Relaxation time, Predvoditelev numbers, dimensionless thermal conductivity, Fourier numbers, Stefan number, solid fraction on temperature, and position of moving interface are discussed in detail.

Meshless approach to the large-eddy simulation of the continuous casting process

The paper discusses the numerical solution of the large-eddy formulation for modelling the turbulent fluid flow with solidification in the continuous casting of steel. This industrially relevant problem is solved by a meshless method for the first time. The solid-liquid system is formulated within the continuum mixture formulation of the governing, mass momentum and energy equations. The Darcy porous media model describes the mushy region. The large-eddy formulation is based on the Smagorinsky model for sub-grid scale viscosity and the van Driest damping function. The synthetic turbulence is prescribed at the molten steel inlet. The generated turbulent fluctuations are isotopic and correlated in time through an asymmetric time filter. Explicit time discretisation, combined with meshless local radial basis function collocation method, is employed. Five-noded subdomains, non-uniform node arrangement and multiquadrics shape functions are used for solving a two-dimensional model. The sensitivity to different node arrangements, time steps, inlet temperature, and velocity boundary conditions is elaborated and successfully verified by comparison with our previously published meshless k − ε turbulence model of the same process.

Implementation of the Marangoni effect in an open-source software environment and the influence of surface tension modeling in the mushy region in laser powder bed fusion (LPBF)

Tangential surface tension forces on a gas–liquid interface due to surface tension gradients have been implemented in the computational fluid dynamics (CFD) solver icoReactingMultiphaseInterFoam provided by the open-source software environment of OpenFOAM OpenCFD Ltd (ESI Group) OpenFOAM (online) https://www.openfoam.com/ (accessed 21 May 2021), so that the Marangoni effect can be taken into account, which is a main driver of heat transfer in additive manufacturing processes that comprise a melt pool. The solver surpasses the capabilities of similar open-source projects by considering a wide range of physical effects, e.g. multiple phases, melting, solidification, evaporation, and laser beam heat sources with an arbitrary intensity distribution and thus makes it an appealing framework, especially for the simulation of the laser powder bed fusion (LPBF) process. Herein, all relevant details and derivation considering the Marangoni effect are provided and validated by means of a benchmark problem by comparing the obtained results with the available analytical solution, with the results obtained from a commercial CFD tool and with the results of other authors. The modified solver is additionally validated by comparing the results from LPBF simulations with experimental data. Furthermore, the influence of the surface tension modeling on the mushy region is investigated. The optimized implementation shows improvements of the simulation results in both the dimensions and shape of the melt pool and the resulting surface with regard to the experimental data.