Freeze casting, a manufacturing technique widely applied in biomedical fields for fabricating biomaterial scaffolds, poses challenges for predicting directional solidification due to its highly nonlinear behavior and complex interplay of process parameters. Conventional numerical methods, such as computational fluid dynamics (CFD), require adequate and accurate boundary condition knowledge, limiting their utility in real-world transient solidification applications due to technical limitations. In this study, we address this challenge by developing a physics-informed neural networks (PINNs) model to predict directional solidification in freeze-casting processes. The PINNs model integrates physical constraints with neural network predictions, requiring significantly fewer predetermined boundary conditions compared to CFD. Through a comparison with CFD simulations, the PINNs model demonstrates comparable accuracy in predicting temperature distribution and solidification patterns. This promising model achieves such a performance with only 5000 data points in space and time, equivalent to 250,000 timesteps, showcasing its ability to predict solidification dynamics with high accuracy. The study's major contributions lie in providing insights into solidification patterns during freeze-casting scaffold fabrication, facilitating the design of biomaterial scaffolds with finely tuned microstructures essential for various tissue engineering applications. Furthermore, the reduced computational demands of the PINNs model offer potential cost and time savings in scaffold fabrication, promising advancements in biomedical engineering research and development.@en

The present study addresses the challenge of enhancing computational efficiency without compromising accuracy in numerical simulations of vacuum gas dynamics using the direct simulation Monte Carlo (DSMC) method. A technique termed 'fixed particle per cell (FPPC)' was employed, which enforces a fixed number of simulator particles across all computational cells. The proposed technique eliminates the need for real-time adjustment of particle weights during simulation, reducing calculation time. Using the SPARTA solver, simulations of rarefied gas flow in a micromixer and rarefied supersonic airflow around a cylinder were conducted to validate the proposed technique. Results demonstrate that applying the FPPC technique effectively reduces computational costs while yielding results comparable to conventional DSMC implementations. Additionally, the application of local grid refinement coupled with the FPPC technique was investigated. The results show that integrating local grid refinement with the FPPC technique enables accurate prediction of flow behaviour in regions with significant gradients. These findings highlight the efficacy of the proposed technique in improving the accuracy and efficiency of numerical simulations of complex vacuum gas dynamics at a reduced computational cost.

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Modeling the thermal and fluid flow fields in laser-based directed energy deposition (DED-LB) is crucial for understanding process behavior and ensuring part quality. However, existing models often fail to accurately predict these fields due to simplifying assumptions, particularly regarding powder particle-induced attenuation in laser power and energy density distribution, and the variable material properties and process parameters. The present work introduces a high-fidelity multi-phase thermal-fluid model driven by a combination of the discrete element method (DEM) and the finite volume method (FVM). Incorporating an enhanced attenuation model for laser energy enables a more precise approximation of powder particle-induced attenuation effects in the laser power and energy density distribution. The study focuses on the influence of laser beam intensity profiles during DED-LB of austenitic stainless steel (AISI 316 L), with model validation conducted through experimental measurements of deposited track dimensions for different beam shapes. The results of numerical simulations demonstrate the critical impact of powder-induced attenuation on the laser power and intensity profiles. Neglecting laser energy attenuation, a common assumption in numerical simulations of DED-LB, leads to overestimations of the absorbed energy of the laser beam, affecting thermal and fluid flow fields, and melt pool dimensions. The present study unravels the complex relationship between the attenuation coefficient (due to the powder stream) and powder stream characteristics, describing the variations of the attenuation coefficient with changes in the powder mass flow rate and powder stream incidence angle. The findings show the critical effects of laser beam shaping on melt pool behavior in DED-LB, with square beams inducing larger melt pool volumes and circular beams creating smaller but deeper melt pools. The proposed enhanced thermal-fluid modeling framework offers a robust approach for optimizing laser-based additive manufacturing across diverse materials and laser systems.

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Solid-liquid phase transformation of a phase change material in a rectangular enclosure with corrugated fins is studied. Employing a physics-based model, the influence of fin length, thickness, and wave amplitude on the thermal and fluid flow fields is explored. Incorporating fins into thermal energy storage systems enhances the heat transfer surface area and thermal penetration depth, accelerating the melting process. Corrugated fins generate more flow perturbations than straight fins, improving the melting performance. Longer and thicker fins increase the melting rate, average temperature, and thermal energy storage capacity. However, the effect of fin thickness on the thermal characteristics seems insignificant. Larger fin wave amplitudes increase the heat transfer surface area but disrupt natural convection currents, slowing the melting front progress. A surrogate model based on an artificial neural network in conjunction with the particle swarm optimisation is developed to optimise the fin geometry. The optimised geometry demonstrates a 43% enhancement in thermal energy storage per unit mass compared to the case with planar fins. The data-driven model predicts the liquid fraction with less than 1% difference from the physics-based model. The proposed approach provides a comprehensive understanding of the system behaviour and facilitates the design of thermal energy storage systems.

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The direct simulation Monte Carlo (DSMC) method, which is a probabilistic particle-based gas kinetic simulation approach, is employed in the present work to describe the physics of rarefied gas flow in super nanoporous materials (also known as mesoporous). The simulations are performed for different material porosities (0.5≤ϕ≤0.9), Knudsen numbers (0.05≤Kn≤1.0), and thermal boundary conditions (constant wall temperature and constant wall heat flux) at an inlet-to-outlet pressure ratio of 2. The present computational model captures the structure of heat and fluid flow in porous materials with various pore morphologies under rarefied gas flow regime and is applied to evaluate hydraulic tortuosity, permeability, and skin friction factor of gas (argon) flow in super nanoporous materials. The skin friction factors and permeabilities obtained from the present DSMC simulations are compared with the theoretical and numerical models available in the literature. The results show that the ratio of apparent to intrinsic permeability, hydraulic tortuosity, and skin friction factor increase with decreasing the material porosity. The hydraulic tortuosity and skin friction factor decrease with increasing the Knudsen number, leading to an increase in the apparent permeability. The results also show that the skin friction factor and apparent permeability increase with increasing the wall heat flux at a specific Knudsen number. @en

A numerical framework based on computational fluid dynamics (CFD), using the finite volume method (FVM) and volume of fluid (VOF) technique is presented to investigate the effect of the laser beam intensity profile on melt pool behavior in laser-assisted powder-based directed energy deposition (L-DED). L-DED is an additive manufacturing (AM) process that utilizes a laser beam to fuse metal powder particles. To assure high-fidelity modeling, it was found that it is crucial to accurately model the interaction between the powder stream and the laser beam in the gas region above the substrate. The proposed model considers various phenomena including laser energy attenuation and absorption, multiple reflections of the laser rays, powder particle stream, particle-fluid interaction, temperature-dependent properties, buoyancy effects, thermal expansion, solidification shrinkage and drag, and Marangoni flow. The latter is induced by temperature and element-dependent surface tension. The model is validated using experimental results and highlights the importance of considering laser energy attenuation. Furthermore, the study investigates how the laser beam intensity profile affects melt pool size and shape, influencing the solidification microstructure and mechanical properties of the deposited material. The proposed model has the potential to optimize the L-DED process for a variety of materials and provides insights into the capability of numerical modeling for additive manufacturing optimization. @en

Laser beam shaping offers remarkable possibilities to control and optimise process stability and tailor material properties and structure in laser-based welding and additive manufacturing. However, little is known about the influence of laser beam shaping on the complex melt-pool behaviour, solidified melt-track bead profile and microstructural grain morphology in laser material processing. A simulation-based approach is utilised in the present work to study the effects of laser beam intensity profile and angle of incidence on the melt-pool behaviour in conduction-mode laser melting of stainless steel 316L plates. The present high-fidelity physics-based computational model accounts for crucial physical phenomena in laser material processing such as complex laser–matter interaction, solidification and melting, heat and fluid flow dynamics, and free-surface oscillations. Experiments were carried out using different laser beam shapes and the validity of the numerical predictions is demonstrated. The results indicate that for identical processing parameters, reshaping the laser beam leads to notable changes in the thermal and fluid flow fields in the melt pool, affecting the melt-track bead profile and solidification microstructure. The columnar-to-equiaxed transition is discussed for different laser-intensity profiles.

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The gas flow characteristics in lid-driven cavities are influenced by several factors, such as the cavity geometry, gas properties, and boundary conditions. In this study, the physics of heat and gas flow in cylindrical lid-driven cavities with various cross sections, including fully or partially rounded edges, is investigated through numerical simulations using the direct simulation Monte Carlo (DSMC) and the discrete unified gas kinetic scheme (DUGKS) methods. The thermal and fluid flow fields are systematically studied for both constant and oscillatory lid velocities, for various degrees of gas rarefaction ranging from the slip to the free-molecular regimes. The impact of expansion cooling and viscous dissipation on the thermal and flow fields, as well as the occurrence of counter-gradient heat transfer (also known as anti-Fourier heat transfer) under non-equilibrium conditions, is explained based on the results obtained from numerical simulations. Furthermore, the influence of the incomplete tangential accommodation coefficient on the thermal and fluid flow fields is discussed. A comparison is made between the thermal and fluid flow fields predicted in cylindrical cavities and those in square-shaped cavities. The present work contributes to the advancement of micro-/nano-electromechanical systems by providing valuable insight into rarefied gas flow and heat transfer in lid-driven cavities.

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Additive manufacturing offers a significant potential for producing metallic parts with distinctly localised microstructures and mechanical properties, commonly known as functional grading. While functional grading is generally accomplished through compositional variations or in-situ thermo-mechanical treatments, variation of process parameters during additive manufacturing can offer a promising alternative approach. Focusing on the electric arc-based additive manufacturing process, this work focuses on the functional grading of high-strength steel (S690 grade) by adjusting the travel speed and inter-pass temperature. Through a combination of thermal simulations and experimental measurements on single bead-on-plate depositions, it is shown that the microstructure and the mechanical properties of parts can be controlled through the rational adjustment of process parameters. A rectangular block was fabricated to demonstrate functional grading using a constant wire feed rate and varying travel speed. The rectangular block consisted of a low heat input (LHI) region deposited between high heat input (HHI) zones. A graded microstructure was obtained with the HHI zones composed of a mixture of polygonal ferrite, acicular ferrite, and bainite, while the LHI region was primarily composed of martensite. The hardness and profilometry-based indentation plastometry measurements indicated that the LHI region exhibited higher hardness (32%) and strength (50%), but lower uniform elongation (80%), compared to the HHI zones. The present study demonstrates the potential to achieve functional grading by adjusting process parameters in electric arc-based additive manufacturing, providing opportunities for tailor-made properties in parts.

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Laser butt welding of thin metal sheets is a widely used fusion-based joining technique in industrial manufacturing. A comprehensive understanding of the complex transport phenomena during the welding process is essential for achieving high-quality welds. In the present work, high-fidelity numerical simulations are employed to investigate the influence of various symmetric and asymmetric welding configurations on the melt-pool behaviour in conduction-mode laser butt welding of stainless steel sheets. The analysis focuses on the effects of laser power density, heat source misplacement and different welding scenarios, including plates with a root gap, high-low mismatches, and dissimilar thicknesses, on the molten metal flow and heat transfer. The results show that advection is the dominant mechanism for energy transfer in the melt pool, and its contribution increases with higher laser power. The non-uniform temperature distribution over the melt-pool surface induces Marangoni shear forces, driving the flow of molten metal and leading to the formation of vortices and periodic flow oscillations within the pool. The effects of various types of asymmetries on the thermal and molten metal flow fields, as well as the process stability, are thoroughly examined and compared with symmetrical welding configurations. These comprehensive simulations provide valuable insights into the fluid flow dynamics and thermal field evolution during laser butt welding of thin metal sheets. The knowledge gained from this study can facilitate process optimisation and guide the improvement of weld quality in practical applications.

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The absorptivity of a material is a major uncertainty in numerical simulations of laser welding and additive manufacturing, and its value is often calibrated through trial-and-error exercises. This adversely affects the capability of numerical simulations when predicting the process behaviour and can eventually hinder the exploitation of fully digitised manufacturing processes, which is a goal of “industry 4.0”. In the present work, an enhanced absorption model that takes into account the effects of laser characteristics, incident angle, surface temperature, and material composition is utilised to predict internal heat and fluid flow in laser melting of stainless steel 316L. Employing such an absorption model is physically more realistic than assuming a constant absorptivity and can reduce the costs associated with calibrating an appropriate value. High-fidelity three-dimensional numerical simulations were performed using both variable and constant absorptivity models and the predictions compared with experimental data. The results of the present work unravel the crucial effect of absorptivity on the physics of internal flow in laser material processing. The difference between melt-pool shapes obtained using fibre and CO2 laser sources is explained, and factors affecting the local energy absorption are discussed.@en

The growing demand for manufactured products with complex geometries requiring advanced fusion-based manufacturing techniques emphasises the importance of process development and optimisation to reduce the risk of adverse outcomes, which is currently impeded with traditional approaches (trial and error experiments). Development, optimisation and qualification of such procedures are often expensive and time-consuming, particularly when new materials or new material combinations are involved. Process stability is intrinsically linked to the stability of the molten metal melt-pool, which ideally should solidify in a smooth and continuous manner to produce a consistent product, free of undesirable geometric and metallurgical defects. The influence of material properties and process conditions on melt-pool stability are generally difficult to derive from experimental observations; hence process optimisation is often reliant on a trial-and-error approach, mitigated to a large extent by a considerable body of industrial experience. The challenge addressed in this research is to develop a simulation-based approach to assess the stability of oscillating melt-pools in fusion welding and additive manufacturing, to minimise the number of trial-and-error experiments required for process development and optimisation, which ultimately will lead to shortening the time between design and production. The computational model developed in the present work has a generic construction with specific process influences addressed through appropriate boundary conditions, avoiding the necessity to integrate melt pool and detailed process descriptions in a single simulation. The model is therefore capable of representing a wide range of welding and additive manufacturing technologies through selection of appropriate material properties and boundary conditions. The robustness of the present computational model in predicting the melt-pool behaviour is demonstrated by comparing the numerical predictions with experimental, analytical and numerical data. Focusing on numerical simulations of solidification and melting using the enthalpy-porosity method, the influence of the permeability coefficient (also known as the mushy-zone constant) on the numerical predictions, which is employed to dampen fluid velocities in the mushy zone and suppress them in solid regions, is systematically analysed for both isothermal and non-isothermal phase-change problems. For isothermal phase-change problems, reducing the cell size diminishes the influence of the mushy-zone constant on the results and the solution becomes independent of the mushy-zone constant for fine enough meshes. Numerical predictions of non-isothermal phase-change problems are inherently dependent on the mushy-zone constant. A method is proposed, based on a Péclet number, to predict and evaluate the influence of the permeability coefficient on numerical predictions of solidification and melting problems. In many numerical studies in the literature, the transport coefficients of the material, specifically thermal conductivity and viscosity, are artificially increased by a so-called `enhancement factor' to achieve agreement between experiments and numerically predicted melt-pool sizes and solidification rates. However, the use of an enhancement factor has little physical meaning, does not represent the physics of complex transport phenomena and can significantly affect the numerical predictions. The effects of using enhancement factors on the numerical predictions of melt-pool behaviour in fusion welding and additive manufacturing are studied in detail. Moreover, the effects of employing temperature-dependent material properties on the numerical predictions are discussed in the present thesis. Melt pools in fusion welding and additive manufacturing exhibit highly non-linear responses to variations of process parameters and are very sensitive to imposed boundary conditions. Temporal and spatial variations in the energy-flux distribution, which are often neglected in numerical simulations, are taken into account in the present work. It is shown how deformations of the melt-pool surface, due to fluid motion as well as changes in the system orientation, affect the numerical predictions of thermal and fluid flow fields. The effects of joint shape design on melt-pool behaviour during fusion welding is also studied in the present work. Changes in power-density and force distributions affect the thermal and fluid flow fields on the melt-pool surface, which in turn can influence the pool shape. Oscillations strongly relate to shape and size of the melt-pool and the surface tension distribution on the molten material surface. Using the simulation-based approach developed in the present work, the frequency and amplitude of melt-pool oscillations and changes in the oscillation modes are predicted, which are not accessible using published analytical models and are generally difficult to measure experimentally. Additionally, using the proposed simulation-based approach, the need for triggering of the melt-pool oscillations is obviated, since even small surface displacements are detectable, which are not sensible to the current measurement devices employed in experiments. The dynamic features of the oscillation signals cannot easily be derived employing conventional Fourier transform (FT) analysis since the oscillation signals are assumed to be stationary (i.e. the behaviour of the system is linear and time-invariant), which is often not the case in fusion welding and additive manufacturing. The continuous wavelet transform (CWT) has been employed in the present work to overcome the shortcomings of the conventional fast Fourier transform (FFT) analysis in characterising the non-stationary features of the surface oscillation signals received from the melt pool. Employing the continuous wavelet transform, the time-resolved melt-pool surface oscillation signals obtained from the numerical simulations can be decomposed into time and frequency spaces simultaneously. The simulation-based approach developed in the present work addresses some of the significant challenges involved in assessing the melt-pool stability for process development and optimisation. The numerical predictions of the present computational model enhances the current understanding of the process behaviour, which is often very challenging to achieve from experiments alone. Moreover, the present simulation-based approach can be employed to explore the design space and reduce the costs associated with process development and optimisation.@en

Development, optimisation and qualification of welding and additive manufacturing procedures to date have largely been undertaken on an experimental trial and error basis, which imposes significant costs. Numerical simulations are acknowledged as a promising alternative to experiments, and can improve the understanding of the complex process behaviour. In the present work, we propose a simulation-based approach to study and characterise molten metal melt pool oscillatory behaviour during arc welding. We implement a high-fidelity three-dimensional model based on the finite-volume method that takes into account the effects of surface deformation on arc power-density and force distributions. These factors are often neglected in numerical simulations of welding and additive manufacturing. Utilising this model, we predict complex molten metal flow in melt pools and associated melt-pool surface oscillations during both steady-current and pulsed-current gas tungsten arc welding (GTAW). An analysis based on a wavelet transform was performed to extract the time-frequency content of the displacement signals obtained from numerical simulations. Our results confirm that the frequency of oscillations for a fully penetrated melt pool is lower than that of a partially penetrated melt pool with an abrupt change from partial to full penetration. We find that during transition from partial to full penetration state, two dominant frequencies coexist in the time-frequency spectrum. The results demonstrate that melt-pool oscillations profoundly depend on melt-pool shape and convection in the melt pool, which in turn is influenced by process parameters and material properties. The present numerical simulations reveal the unsteady evolution of melt pool oscillatory behaviour that are not predictable from published theoretical analyses. Additionally, using the proposed simulation-based approach, the need of triggering the melt-pool oscillations is expendable since even small surface displacements are detectable, which are not sensible to the current measurement devices employed in experiments.
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Gas flow and heat transfer in confined geometries at micro-and nanoscales differ considerably from those at macro-scales, mainly due to nonequilibrium effects such as velocity slip and temperature jump. Nonequilibrium effects increase with a decrease in the characteristic length-scale of the fluid flow or the gas density, leading to the failure of the standard Navier–Stokes–Fourier (NSF) equations in predicting thermal and fluid flow fields. The direct simulation Monte Carlo (DSMC) method is employed in the present work to investigate pressure-driven nitrogen flow in divergent microchannels with various divergence angles and isothermal walls. The thermal fields obtained from numerical simulations are analysed for different inlet-to-outlet pressure ratios (1.5≤Π≤2.5), tangential momentum accommodation coefficients, and Knudsen numbers (0.05≤Kn≤12.5), covering slip to free-molecular rarefaction regimes. The thermal field in the microchannel is predicted, heat-lines are visualised, and the physics of heat transfer in the microchannel is discussed. Due to the rarefaction effects, the direction of heat flow is largely opposite to that of the mass flow. However, the interplay between thermal and pressure gradients, which are affected by geometrical configurations of the microchannel and the applied boundary conditions, determines the net heat flow direction. Additionally, the occurrence of thermal separation and cold-to-hot heat transfer (also known as anti-Fourier heat transfer) in divergent microchannels is explained. @en

Molten metal melt pools are characterised by highly non-linear responses, which are very sensitive to imposed boundary conditions. Temporal and spatial variations in the energy flux distribution are often neglected in numerical simulations of melt pool behaviour. Additionally, thermo-physical properties of materials are commonly changed to achieve agreement between predicted melt-pool shape and experimental post-solidification macrograph. Focusing on laser spot melting in conduction mode, we investigated the influence of dynamically adjusted energy flux distribution and changing thermo-physical material properties on melt pool oscillatory behaviour using both deformable and non-deformable assumptions for the gas-metal interface. Our results demonstrate that adjusting the absorbed energy flux affects the oscillatory fluid flow behaviour in the melt pool and consequently the predicted melt-pool shape and size. We also show that changing the thermo-physical material properties artificially or using a non-deformable surface assumption lead to significant differences in melt pool oscillatory behaviour compared to the cases in which these assumptions are not made.

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Internal flow behaviour and melt-pool surface oscillations during arc welding are complex and not yet fully understood. In the present work, high-fidelity numerical simulations are employed to describe the effects of welding position, sulphur concentration (60-300 ppm) and travel speed (1.25-5 mms-1) on molten metal flow dynamics in fully-penetrated melt-pools. A wavelet transform is implemented to obtain time-resolved frequency spectra of the oscillation signals, which overcomes the shortcomings of the Fourier transform in rendering time resolution of the frequency spectra. Comparing the results of the present numerical calculations with available analytical and experimental datasets, the robustness of the proposed approach in predicting melt-pool oscillations is demonstrated. The results reveal that changes in the surface morphology of the pool resulting from a change in welding position alter the spatial distribution of arc forces and power-density applied to the molten material, and in turn affect flow patterns in the pool. Under similar welding conditions, changing the sulphur concentration affects the Marangoni flow pattern, and increasing the travel speed decreases the size of the pool and increases the offset between top and bottom melt-pool surfaces, affecting the flow structures (vortex formation) on the surface. Variations in the internal flow pattern affect the evolution of melt-pool shape and its surface oscillations.

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One of the challenges for development, qualification and optimisation of arc welding processes lies in characterising the complex melt-pool behaviour which exhibits highly non-linear responses to variations of process parameters. The present work presents a computational model to describe the melt-pool behaviour in root-pass gas metal arc welding (GMAW). Three-dimensional numerical simulations have been performed using an enhanced physics-based computational model to unravel the effect of groove shape on complex unsteady heat and fluid flow in GMAW. The influence of surface deformations on the magnitude and distribution of the heat input and the forces applied to the molten material were taken into account. Utilising this model, the complex thermal and fluid flow fields in melt pools were visualised and described for different groove shapes. Additionally, experiments were performed to validate the numerical predictions and the robustness of the present computational model is demonstrated. The model can be used to explore the physical effects of governing fluid flow and melt-pool stability during gas metal arc root welding. @en

Mixing of high-viscosity liquids (e.g. glycerol–water solutions) is challenging and costly and often requires employing active mixing methods. Two-phase flow micromixers have attracted attention due to their low cost, simple structure, and high performance. In the present work, we investigate the mixing of similar fluids with viscosities equal to or higher than that of water in a two-phase (gas-liquid) slug-flow micromixer, as an economical passive design. Various cases are studied, in which the liquid samples to be mixed are either water or glycerol–water solution. The performance of the proposed slug-flow micromixer is compared with that of a single-phase micromixer with similar geometrical configuration. We demonstrate that mixing efficiencies higher than 90% are attainable for species with viscosities of about 54% higher than that of water (O(10⁻³) kg m⁻¹ s⁻¹); a result that is not attainable in the corresponding single-phase micromixer. Moreover, a mixing efficiency of more than 80% is achieved at the outlet of the micromixer for solutions with viscosities of 160% higher than that of water.

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