© 2024 Elsevier LtdThe thermal characterization of materials at high temperatures is crucial to various modern engineering applications. However, direct experimental measurements under severe conditions can be complex, expensive and offer several other disadvantages. Hence, in this work, a novel Radial Basis Function (RBF) based inverse method is proposed as an alternative to solve nonlinear Inverse Heat Transfer Problems (IHTPs). Here, a proof of concept is performed by estimating a two parameters exponential function describing the specific heat of an AISI 1020 steel submitted to LASER Beam Welding (LBW). An inverse algorithm combined with an RBF interpolation algorithm enables an enhanced search domain scan. A least squares objective function with Future Time Regularization (FTR) is implemented to govern the estimation. The algorithms are sequentially run and refeed to refine the minimization region through adjustable search factors. A Finite Volume Method (FVM) thermal model was implemented through a highly parallelized inhouse CUDA-C code, run on an Nvidia Geforce® RTX™ 3090. A verification was performed using three commercial solutions. The method's efficiency was demonstrated with both noiseless and variable standard deviation data. The approach is less sensitive to local minima than previous Quadrilateral Optimization Method (QOM), with estimation errors below 1.0 % in nearly all cases.

© 2025, Begell House Inc. All rights reserved.This study presents an in-depth comparative analysis with a widely used turbulence model in Computational Fluid Dynamics (CFD): the standard k-ε model. The research focuses on turbulent flow over a backward-facing step (BFS), a classical problem known for its complex recirculation and reattachment phenomena. Simulations were conducted using both an innovative Graphics Processing Unit (GPU) based parallel processing algorithm developed on the Nvidia Compute Unified Device Architecture (CUDA) platform, and a Central Processing Unit (CPU) based commercial software. The numerical simulation analysis spans a broad range of Reynolds numbers, representing different levels of turbulence intensity, and compares the performance of these two approaches. The primary objective of this study is to evaluate the predictive capabilities of the standard k-ε model in terms of reattachment length, a critical parameter for accurately capturing the dynamics of separated flows. The simulation results obtained from both software platforms are rigorously compared with classical experimental data at ReH = 36,000 to assess the accuracy and reliability of each approach. The GPU simulations were performed on an Nvidia GeForce RTX™ 3090Ti with 24 GB of video memory, while the commercial simulations were run on an Intel®Core™ i7-12700H CPU, featuring a 2.3 GHz base clock and 14 cores. The results indicate that GPUs offer a more optimal architecture for CFD problem-solving, leveraging large-scale computational parallelization.

© 2025, Begell House Inc.. All rights reserved.This study presents a numerical investigation of Von Karm an flow at a Reynolds number of 200, induced byflow past a single cylinder. The Von Karm an vortex street, characterized by alternating vortices shed froma bluff body, is a fundamental phenomenon in fluid dynamics with significant applications in engineering systems. We employ the Finite Volume Method (FVM) to discretize the governing Navier-Stokes equations, capturing the intricate interactions within the velocity field surrounding the cylinder. Computations are performed using Graphics Processing Units (GPUs) to leverage their parallel processing capabilities. The GPUaccelerated FVM achieves a computational speedup of 50 times compared to traditional calculations on an Intel i9 CPU. This substantial acceleration enables high-resolution simulations that provide deeper insights into the flow structures of the system. The results demonstrate the effectiveness of GPU computing in solving complex fluid dynamics problems and highlight its potential to advance research in computational fluid dynamics.

© 2025, Begell House Inc.. All rights reserved.This study presents an in-depth examination of a three-dimensional conjugate heat transfer (CHT) model within a cubic cavity containing a solid cubic insert, engineered to investigate the thermal interaction at the fluid-solid interface. The thermal gradient induced across the cavity’s walls initiates fluid motion via natural convection, effectively modeled using the Boussinesq approximation to address the fluid’s thermally induced density variations. Central to this research is the development of an innovative CHT approach that employs a coupled boundary condition, integrating the heat conduction equations of the solid and the thermal-fluid dynamics equations of the fluid into a seamless analytical framework. This integration not only facilitates a comprehensive analysis of the fluid-solid interface but also enhances the accuracy and coherence of the simulation results. By treating the solid and fluid components as interconnected systems through the coupled boundary condition, the study demonstrates significant improvements in the predictability of temperature distribution and flow patterns within the cavity. Validation against established benchmarks confirms the model’s superior capability in capturing complex interactions at the fluid-solid boundary, highlighting its potential to advance thermal management strategies across a variety of engineering applications. The paper underscores the efficiency and reliability of the new approach, showcasing its value in providing more detailed insights into the intricate dynamics of heat transfer and fluid movements, crucial for optimizing design processes in both academic research and industrial practice.

© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.The root pass represents a challenge for welders. Being the first pass of the joint, it requires full penetration and is more prone to metallurgical defects. There needs to be a balance between the forces acting on the molten pool to avoid incomplete penetration or burnthrough. Additionally, the hardness in the heat affected zone (HAZ) should not exceed 350 HV, beyond which there is susceptibility to cold cracking. When different thicknesses are present in the joints, it is often thought that greater thicknesses require higher welding energy (the ratio between power and welding speed). This has also been verified in the literature. The present work aims to test if it be possible to weld the root pass of four plates of different thicknesses (7 mm, 10 mm, 12.7 mm, and 25.4 mm) considering a similar welding energy. This would make the parameterization robust, as the welder would not need to change the welding energy to perform the process under different conditions. An experimental evaluation was conducted on shipbuilding steel ASTM A131 DH36 using the GMAW process, evaluating both the geometric characteristics of the weld bead and the microstructure at different thicknesses. Cooling rates were predicted based on an in-house finite volume method (FVM) computational code. The results indicated that although all welds met the main requirement of full penetration, the metallurgical requirement of a maximum hardness of 350 HV in the HAZ was only achieved at thicknesses of 7 mm and 10 mm. This occurred because, in greater thicknesses (12.7 mm and 25.4 mm), the cooling rate was elevated due to the thickness itself and the use of a higher feed rate. Consequently, in the coarse grain heat affected zone (CGHAZ), there was a shift from the ferritic field to the bainitic field. To meet the requirements, it is advisable to adjust parameters, such as increasing weld energy or applying preheat treatment. Another alternative involves planning subsequent passes to induce a tempering effect on the root. In summary, for geometrical purposes, a constant energy can be used, whereas metallurgical objectives might necessitate greater energy input with increasing thickness.

© 2024 by the authors.This research develops an innovative framework for accelerating Conjugate Heat Transfer (CHT) simulations within squared heated cavities through the application of Graphics Processing Units (GPUs). Although leveraging GPUs for computational speed improvements is well recognized, this study distinguishes itself by formulating a tailored optimization strategy utilizing the CUDA-C programming language. This approach is specifically designed to tackle the inherent challenges of modeling squared cavity configurations in thermal simulations. Comparative performance evaluations reveal that our GPU-accelerated framework reduces computation times by up to 99.7% relative to traditional mono-core CPU processing. More importantly, it demonstrates an increase in accuracy in heat transfer predictions compared to existing CPU-based models. These results highlight not only the technical feasibility but also the substantial enhancements in simulation efficiency and accuracy, which are crucial for critical engineering applications such as aerospace component design, electronic device cooling, and energy system optimization. By advancing GPU computational techniques, this work contributes significantly to the field of thermal management, offering a potential for broader application and paving the way for more efficient, sustainable engineering solutions.

© 2024 by the authors.Thermally characterizing high-thermal conductivity materials is challenging, especially considering high temperatures. However, the modeling of heat transfer processes requires specific material information. The present study addresses an inverse approach to estimate the thermal conductivity of SAE 1020 relative to temperature during an autogenous LASER Beam Welding (LBW) experiment. The temperature profile during LBW is computed with the aid of an in-house CUDA-C algorithm. Here, the governing three-dimensional heat diffusion equation is discretized through the Finite Volume Method (FVM) and solved using the Successive Over-Relaxation (SOR) parallelized iterative solver. With temperature information, one may employ a minimization procedure to assess thermal properties or process parameters. In this work, the Quadrilateral Optimization Method (QOM) is applied to perform estimations because it allows for the simultaneous optimization of variables with no quantity restriction and renders the assessment of parameters in unsteady states valid, thereby preventing the requirement for steady-state experiments. We extended QOM’s prior applicability to account for more parameters concurrently. In Case I, the optimization of the three parameters that compose the second-degree polynomial function model of thermal conductivity is performed. In Case II, the heat distribution model’s gross heat rate (Ω) is also estimated in addition to the previous parameters. Ω [W] quantifies the power the sample receives and is related to the process’s efficiency. The method’s suitability for estimating the parameters was confirmed by investigating the reduced sensitivity coefficients, while the method’s stability was corroborated by performing the estimates with noisy data. There is a good agreement between the reference and estimated values. Hence, this study introduces a proper methodology for estimating a temperature-dependent thermal property and an LBW parameter. As the performance of the present algorithm is increased using parallel computation, a pondered solution between estimation reliability and computational cost is achieved.

© 2024 by the authors.The maximum number of parallel threads in traditional CFD solutions is limited by the Central Processing Unit (CPU) capacity, which is lower than the capabilities of a modern Graphics Processing Unit (GPU). In this context, the GPU allows for simultaneous processing of several parallel threads with double-precision floating-point formatting. The present study was focused on evaluating the advantages and drawbacks of implementing LASER Beam Welding (LBW) simulations using the CUDA platform. The performance of the developed code was compared to that of three top-rated commercial codes executed on the CPU. The unsteady three-dimensional heat conduction Partial Differential Equation (PDE) was discretized in space and time using the Finite Volume Method (FVM). The Volumetric Thermal Capacitor (VTC) approach was employed to model the melting-solidification. The GPU solutions were computed using a CUDA-C language in-house code, running on a Gigabyte Nvidia GeForce RTX™ 3090 video card and an MSI 4090 video card (both made in Hsinchu, Taiwan), each with 24 GB of memory. The commercial solutions were executed on an Intel® Core™ i9-12900KF CPU (made in Hillsboro, Oregon, United States of America) with a 3.6 GHz base clock and 16 cores. The results demonstrated that GPU and CPU processing achieve similar precision, but the GPU solution exhibited significantly faster speeds and greater power efficiency, resulting in speed-ups ranging from 75.6 to 1351.2 times compared to the CPU solutions. The in-house code also demonstrated optimized memory usage, with an average of 3.86 times less RAM utilization. Therefore, adopting parallelized algorithms run on GPU can lead to reduced CFD computational costs compared to traditional codes while maintaining high accuracy.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.Conjugate heat transfer plays a crucial role in numerous engineering applications, such as thermal management of electronic devices, aerospace heat shields, and energy systems. This paper explores the utilization of Graphics Processing Units (GPUs) and the CUDA-C programming language for solving conjugate heat transfer problems. Three distinct heat transfer scenarios are investigated: the Lid-Driven cavity, squared cavity with natural convection, and squared cavity with a solid square embedded in the center. These problems are solved using numerical methods and parallelized using GPU computing techniques to enhance computational efficiency and reduce simulation time. The Lid-Driven cavity problem involves the flow of a fluid within a square enclosure, where one side is subjected to a constant velocity boundary condition. In the squared cavity with natural convection, the study focuses on heat transfer phenomena occurring due to density-driven fluid motion. The buoyancy effects induce convective currents within the cavity, influencing the temperature distribution. The squared cavity with a solid square in the center represents a more complex conjugate heat transfer problem. The presence of the solid square influences the flow patterns and temperature distribution within the cavity. Through the utilization of GPUs and CUDA-C programming, the computational efficiency of solving conjugate heat transfer problems is greatly enhanced. The parallel processing capabilities of GPUs enable accelerated simulations, reducing the time required for solving these complex problems. The study demonstrated that the proposed algorithm achieved up to 99.7% reduction in simulation time for the laminar lid-driven cavity problem. The results obtained from the simulations provide valuable insights into the heat transfer characteristics, facilitating the optimization of thermal management systems and the design of more efficient heat exchangers. Overall, this study demonstrates the effectiveness of GPU computing in tackling conjugate heat transfer problems and its potential for advancing the field of thermal sciences.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.The recent advancements in computer hardware opened new doors to the modeling and simulation of intensive Computational Fluid Dynamics (CFD) problems. The advent of modern Graphics Processing Units (GPUs) made parallel computing easier by allowing cards to run multiple kernels in several parallel threads with double-precision. However, traditional CFD codes still lack hardware usage optimization due to a low threads scalability computing methodology. Hence, a computational performance investigation between codes run on GPU and Central Processing Unit (CPU) is presented in this work. The analysis was focused on the three-dimensional simulation of a Laser Beam Welding (LBW) process with a moving heat source and non-linear thermal properties. The solutions were developed by applying the Finite Volume Method (FVM) to solve the transient heat conduction Partial Differential Equation (PDE). The phase change was accounted through the enthalpy method. A time and space-dependent Gaussian conical volumetric profile was used to model the heat source. The GPU solutions were computed by a CUDA-C in-house code running on a Nvidia Geforce RTX™ 3090 and RTX™ 4090 video cards, both with 24 GB of memory. Three equivalent solutions were produced by top-rated commercial codes. All codes were run on an Intel® Core™ I9 12900KF CPU with 3.6 GHz base clock and 16 cores. The results evidenced that GPU and CPU processing are similarly precise but GPUs can achieve far faster and more power efficient CFD solutions. The GPU code demonstrated better memory optimization when simulating LBW.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.In the present study, the Quadrilateral Optimization Method (QOM) is applied for parameter estimation in an inverse heat transfer problem. A numerical LASER Beam Welding (LBW) experiment of SAE 1020 is the baseline for the estimations. The temperature-dependent thermal conductivity of the steel is assessed. The algorithm accounts for the conductivity as a second-degree polynomial function of temperature. The three parameters of the function are simultaneously assessed. The method regularizes the objective function through Future Time Regularization (FTR) to account for the temporal analysis. Hence, the effect of using different numbers of time steps was analyzed. The most accurate results were found when considering 60 points. Thus, this configuration was set to expand the algorithm to assess the gross heat rate provided by the LASER along with the thermal conductivity function. The results are sensitive enough to represent reliable assessments. Considering the reference and estimated values, the simulated temperatures show good agreement. The present algorithm requires low computational cost due to a GPU’s parallel computation.

© 2024 Begell House Inc.. All rights reserved.This study introduces NEMESYS, a novel algorithm designed to exploit the parallel processing capabilities of Graphics Processing Units (GPUs) to significantly enhance computational efficiency in fluid dynamics simulations. NEMESYS integrates the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ε turbulence model, and its efficacy is validated through simulations of two classical flow scenarios: laminar flow around a cylinder, exhibiting von Kármán vortex shedding, and turbulent flow over a backward-facing step. The algorithm's performance is critically assessed against established benchmarks from scientific literature and leading commercial Computational Fluid Dynamics (CFD) software. Key performance metrics include the Strouhal number for the cylinder flow and reattachment length for the backward-facing step flow. Results demonstrate remarkable accuracy and reliability of NEMESYS, with a notable reduction in computation time – up to 99.5% faster than traditional CPU-based software. This substantial reduction in computational effort presents significant cost savings and opens new avenues for real-time analysis and accelerated design processes. The implications of this advancement are far-reaching, offering transformative potential for various engineering domains, such as automotive, civil, and environmental engineering, thereby redefining approaches to fluid dynamics analysis and design.

© 2024 Begell House Inc.. All rights reserved.In the field of Computational Fluid Dynamics (CFD), solving conjugate heat transfer problems involving natural convection remains a computationally demanding endeavor. This study presents the NEMESYS algorithm, specifically optimized for Graphics Processing Units (GPUs), with an application focused on natural convection in a square cavity that incorporates a centrally situated solid block. This complex configuration necessitates the concurrent resolution of the Navier-Stokes equations governing fluid flow and the energy equation governing heat conduction in both fluid and solid phases. Through the efficient utilization of GPU-based parallel processing, the NEMESYS algorithm managed to markedly reduce the computational burden. A quantifiable 99.5% time reduction was recorded when compared to equivalent Central Processing Unit (CPU)-based simulations, thereby manifesting a significant leap in computational efficiency. To authenticate the algorithm's credibility, an exhaustive validation process was undertaken. The simulation results were cross-verified against established benchmarks from academic literature as well as outputs from widely used commercial CFD software packages. This validation revealed strong agreement in critical parameters such as fluid velocity and temperature distributions within the fluid cavity, as well as heat conduction characteristics within the solid block. In summary, the NEMESYS algorithm emerges as a reliable, efficient computational framework for tackling the intricacies of natural convection problems involving conjugate heat transfer and holds potential for broader adaptability in high-fidelity CFD simulations.

© 2023 Taylor & Francis Group, LLC.Modern engineering applications use processes that submit materials to high-temperature gradients. However, the traditional experimentation methods applied to determine thermal properties often do not provide reliable data when working temperatures are up to extreme conditions. Hence, the present work demonstrates the use of an inverse heat conduction problem methodology for estimating the thermal properties of a laser beam welding (LBW) process. The applied technique is the quadrilateral optimization method (QOM), which consists of a multivariable estimation approach developed to calculate the function’s parameters. Additionally, the future time regularization scheme was implemented in the objective function to regularize the results. The applied numerical process solved the energy equation using the finite volume method implemented in an in-house CUDA-C language code. The software is a multi-thread application run in a graphics processing unit for enhanced computational time efficiency. A validation study compared the estimated results with LBW simulated data. The QOM estimates the parameters of a function representing the range of thermal conductivity values. The proposed method is expected to lower experimental costs for obtaining thermal properties at high temperatures by eliminating the need for sophisticated technical equipment and skilled labor required by traditional direct measurements.

© 2023 Elsevier LtdIn the field of heat transfer, inverse problems deal with the estimation of parameters that are difficult to measure directly. The usefulness of inverse techniques is such that, due to severe conditions, direct measurement of a certain variable becomes inaccessible. This works aims to perform inverse estimation in two problems. The first case is related to the estimation of the heat flux boundary condition and thermal contact resistance between two SAE 1020 steel plates. The first case is used as validation for the second case and is solved using the finite volume method for the discretization of the diffusion equation and Successive Over Relaxation (SOR) for solving the system of linear eqs. A set of seven one-dimensional experiments were performed varying the roughness and contact pressure at the interface of the samples and, as expected, it was found that the thermal conductance is a function of these parameters. The second case consists in the estimation of three thermal resistances in an aircraft embedded system consisting of four components and ambient air. In this case, the direct problem is solved using fourth-order Runge-Kutta to solve the system of ODEs. In both cases a future times regularization technique approach combined with Markov Chain Monte Carlo (MCMC) optimization method is used to solve the inverse problem. The embedded system inverse problem is also solved using a new and simple approach based on the Quadrilateral Optimization Method (QOM) with future time steps regularization and the result is compared with the MCMC method. The results of this work consolidate a low-cost inverse estimation setup and attest to the capacity of multivariate estimation in inverse heat transfer problems.

© 2023In this work, a methodology is presented to simulate heat transfer in wellbores for plugging & abandonment operations, where the thermal input is provided by a thermite reaction. The operation of burning a thermite column inside the well's production tubing to form a metal plug is studied. The objective is to eliminate the need to simulate the thermite domain and chemical reaction during the process, simplifying the physical model and reducing computational cost. In this model, it is assumed that the thermal input from the thermite reaction is provided to the model through multiple heat flux boundary conditions along the inner wall of the production tubing. The unknown heat flux from the thermite to the inner wall of the tube is estimated by solving an inverse heat conduction problem (IHCP). The Adaptive Function Specification Method is used to estimate multiple heat flux functions at the boundary through information from multiple temperature sensors located on the outer surface along the tube's height. A characteristic behavior of the heat flux curve was verified in all segments of the tube, and the average heat flux curve was used to simulate heat transfer during a 15 m thermite burning process inside a well.

© 2023The advancement of Plug and Abandonments (P&A) procedures is pivotal for reducing the costs associated with current operations. A novel technology concept proposes a heat emitter that will produce enough energy to melt the casing steel without critically affecting the cement layer. However, recent studies concerning this proposal have not given enough attention to the potential impact on the primary cement, which is a crucial material to guarantee the plug's integrity. This study models the heat emitter as a thermite mixture with constant volumetric heat generation, and the oil well structure was approached as a 2-D axisymmetric domain. The finite volume method with a static melting/solidification model is employed to solve the governing equations numerically. A C++ code was developed and compared with the commercial software Ansys® Fluent was performed to verify the present code. The thermal parameters of the heat emitter, including density (1983.6 and 2192.4 kg m−3), specific heat (919.6 and 1016.4 J kg−1 K−1), conductivity (5 and 15 W m−1 K−1), latent heat (1267.79 and 1147.05 kJ kg−1), volumetric heat generation (104.59 and 115.6 MW m−3), and reaction time (71.25 and 78.75 s), are evaluated through a 26 factorial design. The responses analyzed are the maximum melted volume of steel and the volume of cement critically affected. The high variability associated with thermal conductivity indicated a strong dependence on this parameter. Most importantly, this study highlights that melting the casing steel could unintentionally degrade the cement layer, increasing potential leakages paths and integrity problems.

© 2023 by the authors.Implementing input parameters that match the experimental weld shape is challenging in LASER beam welding (LBW) simulation because the computed heat input and spot for temperature acquisition strongly affect the outcomes. Therefore, this study focuses on investigating the autogenous LBW of AISI 1020 using a three-dimensional heat transfer model that assumes a modified Gaussian heat flux distribution depending on LASER power (Qw), radius (R), and penetration (hp). The influence of such variables on the simulated weld bead was assessed through analysis of variance (ANOVA). The ANOVA returns reliable results as long as the data is normally distributed. The input radius exerts the most prominent influence. Taguchi’s design defined the studied data reducing about 65% of the simulations compared to a full factorial design. The optimum values to match the computed outcomes to lab-controlled experiments were 2400 W for power (80% efficiency), 0.50 mm for radius, and 1.64 mm for penetration. Moreover, the experimental errors regarding thermocouples positioning were corrected using linear interpolation. A parallel computing algorithm to obtain the temperature field reduces computational costs and may be applied in real-world scenarios to determine parameters that achieve the expected joint quality. The proposed methodology could reduce the required time to optimize a welding process, saving development and experimental costs.

© 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.Welding processes are a fundamental part of modern engineering manufacturing. The simulation of materials joining techniques requires the application of thermal models capable of mathematically describing the applied heat source distribution. Many different approaches have been developed since the beginning of the CFD revolution. However, one of the most important published works regarding the review and detailing of heat source models was performed almost two decades ago. Hence, the present work was developed specifically focusing on organizing, cataloging, describing, and statistically quantifying the most relevant models already published, with a special focus on the techniques developed in the last twenty years. The reviewed approaches were individually listed concerning their most common applications and limitations. The gathered data includes classified details and condensed information about scientific references, the suitability of each model, and the welding heat source thermal modeling terminology. Additionally, each modeling form was geometrically illustrated in coupling with its equations for an enhanced description and comparison of the geometrical parameters and its expected resultant temperature distributions. The reviewed papers were quantified and statistically enumerated by modeling methodology, welding process type, and number of published works by year. The approaches were also organized chronologically and visually illustrated in a welding heat source modeling timeline. Lastly, the most relevant achievements of the last decades, the research trends, and possibilities for future review works in the field were discussed.

© 2023Recently, there was an increase in the study of phase change materials mainly due to thermal storage studies or modeling of manufacturing processes. Usually, these problems, which have a moving boundary, are solved with the enthalpy formulation. This paper presents a new methodology to address the unsteady enthalpy term in the heat diffusion equation. The Volumetric Thermal Capacitor method is developed to solve the non-linear heat diffusion equation with the enthalpy function. The alternative method applies the integration by parts rule to divide the enthalpy term into three components. This approach allows the use of non-linear thermal properties without simplifications or generalized considerations. The method is compared to the classical formulation. The routines were implemented and executed in parallel on a CUDA-C in-house code. Simulated and lab-controlled experiments validated the proposed methodology. The results highlighted the differences between the models for experiments with intense heat flux. The proposed model presented a better agreement with the experimental data than the classical model for high-temperature cases. The Volumetric Thermal Capacitor method proved to be more stable and accurate than the classical method.

© 2023, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Real-time fluid engineering simulations require significant computational power and high-resolution grids to ensure accuracy. This paper proposes a novel CUDA-C-based simulation algorithm nemesys that leverages GPU devices to solve the Navier-Stokes equations with precision and speed. The algorithm uses a Successive Over Relaxation (SOR) iterative process on a multi-dimensional CUDA core to accelerate solving speed. The co-located Rhie and Chow interpolation scheme is applied to unstructured grids to solve the equations using an implicit finite volume method. Benchmark simulations are performed on two problems aimed to validate the effectiveness of the proposed methodology: the classical lid-driven cavity and closed-channel flow. Results exhibit a significant advantage of the proposed method in terms of convergence rate compared to state-of-the-art techniques using varying grid resolutions and Reynolds numbers. Specifically, the strategy is nearly 850 times faster than parallel CPU-based code when utilizing an RTX 3090 Nvidia graphics card. Furthermore, the algorithm's performance is investigated on an airfoil simulation, confirming the approach's effectiveness. The findings highlight that GPU-based parallel programming is a promising approach for achieving realtime simulations, and the proposed algorithm presents a significant improvement over CPU-based techniques.

© 2022 Elsevier Masson SASA numerical-experimental methodology is presented in this study to estimate the absorption efficiency in a laser welding process by estimating the rate of energy transferred to a metal plate. The iterative Function Specification Method was modified to account for moving temperature sensor thermal sensitivity as a function of time and position relative to the welding bead. Thus, highly nonlinear problems can be solved by using a high-temperature gradient in the measurement sensor region. Three experiments on an AISI 1020 steel sheet were carried out using a 3 kW fiber laser and a 3 m/min welding speed. A thermo-fluid model was used with solid–liquid phase changes, buoyancy forces, and the Marangoni effect in the welding pool to model the physical phenomena. A code in Matlab was developed to solve the inverse problem. The direct problem was solved using COMSOL Multiphysics through the Livelink for Matlab feature. The average absorption efficiency was 79.5% for the welding process. A comparison was made between the geometry of the welding bead obtained in experiments with the numerically calculated welding bead to validate the model. The results obtained in this article are intended to assist simulations in laser welding processes and are in agreement with the literature data.

© 2022 The Authors.The nonlinear thermophysical properties significantly affect the temperature field and the appearance of the weld bead in the LASER Beam Welding (LBW). Then, it is vital to have a well-defined numerical model for analyzing the thermal behavior of the welded material. Nonetheless, many papers still address the welding simulation using constant thermal properties. In this way, this paper proposes a three-dimensional thermal analysis of an unsteady LBW aiming to compare the difference between the constant and nonlinear thermophysical properties approaches. It applied the Finite Volume Method (FVM) to solve the nonlinear three-dimensional heat diffusion equation with an enthalpy function to model the phase change using a fully implicit scheme. In traditional models, these considerations promote a significant increase in computational time for the convergence of the method. Thus, CUDA-C in-house parallel routines were implemented and executed in a Graphics Processing Unit (GPU) to solve this problem. Lab-controlled experiments validated the proposed methodology. The results highlighted the importance of using the nonlinear approach. Furthermore, a detailed study demonstrated the difficulty of knowing precisely the placement of thermocouples, given the high-temperature gradient in the welding processes. The proposed methodology demonstrated to be a faster, cheaper, and efficient way to simulate the LBW.

© 2022, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.In welding processes, many factors contribute in achieving a required quality of the welds. Those factors are numerous and they may interact with each other, affecting response parameters such as welding penetration and the heat-affected zone (HAZ) size. Some factors are more important while the influence of others is negligible. To find an optimum factor combination in order to maximize penetration and minimize the HAZ is not an easy task. This contribution is aimed to evaluate the influence of welding energy (E) versus the influence of current (I) and welding speed (Vw) on the penetration and HAZ volume in the autogenous tungsten inert gas welding process. For this purpose, two numerical models are proposed. The first considers an in-house finite volume numerical model, and the second is based on response surface method. A sensitivity analysis of the proposed numerical model using two strategies is also performed. In addition, to determine the best-operating conditions, a multi-objective optimization problem is proposed and solved. The presented numerical models were found to provide good concordance in terms of coefficient of determination and p-value, indicating its significance. Each model (with one or more independent variables) represents detailed information about the physical process and can be used for optimization. The sensitivity analysis demonstrates that the current affects penetration and HAZ volume much stronger than the welding speed does. Physically, this is due to the fact that the current has linear (arc coupling) and non-linear (Joule effect and pressure gradient) influence, and the welding speed contributes linearly, modulating the heat conduction. Finally, it was demonstrated a compromise between the penetration and the HAZ volume by addressing multi-objective optimization. In this context, point C (I = 250 A; Vw = 24.8 cm/min) of the Pareto curve is the optimal option for operation since it provides a lower relative HAZ volume while keeping the same penetration and higher productivity (welding speed).

© 2021 Elsevier LtdThe actual experimental methods applied to determine the materials' thermal properties at high temperatures usually do not provide good quality values for matching simulations to experimental data. To solve this problem, this work proposes an alternative inverse methodology to estimate the thermal properties of a material at high temperatures. The developed technique is called Quadrilateral Optimization Method (QOM). The QOM is a multivariable estimation technique developed to determine the function's parameters. To regularize the results, the Time Traveling Regularization (TTR) was applied in the objective function. To prove the methodology efficiency, the specific heat is estimated through this inverse approach for a LASER welding problem. In this case, the specific heat was treated as an exponential function. Then, the QOM estimates the parameters of this function. A sensitivity analysis is performed to determine the estimation range. To minimize the computational time, in the direct model the non-linear heat diffusion equation was solved through the Finite Volume Method in an in-house CUDA-C code. A numerical welding experiment was performed to eliminate the real experimental errors. The results demonstrated that the proposed approach had an average error of less than 0.075% in the parameters' estimation in the best-case-scenario. The new methodology was validated, and it proved to be an easier and cheaper way to determine the thermal properties at high temperatures without the need to use advanced experimental apparatus.

© 2021 Elsevier B.V.The use of remelting as heat treatment for metallic components has grown on an industrial scale, particularly in sectors where surface hardness is a requirement. Using a conventional Tungsten Inert Gas (TIG) welding torch, it is possible to induce desirable microstructures, promote grain refinement, and as a result, increase hardness. However, one of the main challenges concerns understanding the effects of remelting strategies based on the torch/tool path planning. It is possible to draw different conclusions under the same processing parameters depending on the tool's trajectory. Therefore, the present study aims to assess the influence of remelting path strategies on the AISI 1045 steel hardness, correlating its microstructure with thermal variables obtained from an in-house Finite Volume numerical model. Two different approaches are analyzed, namely Strategy 1 and Strategy 2.The former was characterized as a single direction movement with 77 s average time between beads, while Strategy 2 was chosen as double direction movement (zigzag) without interbead time. In both cases, TIG remelting was applied autogenously with 120A Direct Current Electrode Negative (DC-), at 15 cm/min, with a 30% overlap ratio for five parallel beads, and with Argon as shielding gas. The results pointed out that both strategies promoted a hardness increase relative to the base metal, 23% for Strategy 1 and 9% for Strategy 2. This factor was attributed to grain refining. The simulation revealed that Strategy 1 is more suitable than Strategy 2 to boost the hardness is related to the higher solidification cooling rate (166 °C/s versus 137 °C/s, respectively) and lower time above 900 °C (7 s versus 12 s, respectively).

© 2021Anisotropic characteristics of certain materials can be used as a design asset in several fields of research and industry. Anisotropic thermal conductivity data available in the literature are limited. This work proposes an alternative experimental methodology to determine the thermal conductivity of anisotropic materials. In the suggested apparatus, samples are settled in a vacuum chamber to assure convective insulation; aluminum films, fixed on the surrounding walls, achieved radiative insulation. To validate the methodology, the research determined the thermal conductivities of known isotropic materials, such as stainless steel, copper, and aluminum. The investigation compared the measured experimental data to the literature ones, which exhibits good coincidence, thus validating the technique. In addition, the study experimentally investigated a phenol-formaldehyde resin reinforced by the presence of cotton fibers called Celeron-C1001. The analysis describes the Celeron-C1001 anisotropic thermal conductivity coefficients by the use of experimentally assessed temperature fields and heat fluxes.

© 2021, The Brazilian Society of Mechanical Sciences and Engineering.Temperature measurement in welding constitutes relevant information for process understanding and simulation, as it can be used to validate and predict microstructure. Monitoring can be performed at specific points through transducers. The typical one is the thermocouple. In laser welding processes, due to the high energy concentration of the beam, the acquisition with thermocouples should be performed closer to the bead when compared to electric arc welding processes. This measurement is critical because of overheating by spatters, which can result in damage. The present work covers developing a Capacitive Discharge Welding device for thermocouple fixing and assessing possible temperature acquisition positions in keyhole laser welding. The study performed all tests with a fiber laser of 9 kW power and 3 m/min scanning speed. When placed at 2 mm from the weld centerline, the results showed a high probability of spattering due to the 71° range of incidence angle. Therefore, the thermocouple should be placed far from the weld centerline to minimize the spattering. However, it must be close enough to acquire temperatures above 727 °C. This temperature corresponds to the envisaged austenitization microstructure correlation. The study found the maximum distance at 3.5 mm based on an interpolation map, where the incidence spatters angle reduced to 59°. At a 2 mm distance from the weld centerline, the weld cross section temperatures reached more than 727 °C. However, the microstructural changes did not occur due to insufficient austenitization time. The Heat Affected Zone boundary was at 1.64 mm from the weld centerline. Therefore, to correlate microstructure with thermal cycles, it is necessary to place thermocouples at a distance below this value. However, spatter can be a problem since the range of incidence angle is about 75°. Therefore, this work recommends using more than one thermocouple for each position (redundancy) to increase valuable data. Graphic abstract: [Figure not available: see fulltext.].

© 2020The estimation of the imposed heat rate in welding processes has always been an obstacle to improve the thermal efficiency of these processes. Thus, the use of inverse problem techniques is an alternative procedure to estimate the heat rate. In this study, the problem is highly nonlinear; therefore, the heat flux provided by the welding process is estimated by the iterative Function Specification method. This method was modified to estimate the heat supply based on the heat rate sensitivity coefficient, which represents the influence of the welding power in the temperatures of 304 stainless steel plates. In order to avoid the problem of low thermal sensitivity due to the movement of the welding source on the upper face of the plate, this methodology is based on the concept of temperature moving sensor. The software COMSOL was used to solve the three-dimensional heat diffusion equation with enthalpy function to model the phase change problem. 10 type K thermocouples, equally spaced, were attached by capacitive discharge on the opposite heated surface to measure the temperature. The efficiency of the process was calculated with the estimated net heat rate which ranged from 63% to 87%. The average efficiency obtained was 75% for this welding process. A relation between the energy rate given by the power supply and the estimated efficiency was also observed. The thermal efficiency of the arc decreases as the power increases. Thus, an analysis using the Taguchi method was performed in order to better understand the influence of the welding parameters on the efficiency of the process. It was concluded that with a significance level of 10%, the welding current and arc length have a strong correlation with thermal efficiency. These results are discussed and compared with results obtained experimentally by other researchers. Besides, an uncertainty analysis in the estimated heat rate is also presented.

© 2020 Elsevier Masson SASWhen the oil and gas extraction in a well is over or ended by wellbore issues, a Plugging and Abandoning (P&A) operation is required. The usual method is the well cementation. A recent process is the rock fusion method through a thermite reaction for wellbore buffering operation. This paper presents a numerical thermal study for this new process. The developed model is based on the solution of the three-dimensional heat diffusion equation by a seven points Finite Difference scheme. A multi-layer geometry, composed of dolomite, cement, carbon iron steel, and thermite, is used to simulate the oil well. The phase change problem is approached through the enthalpy function. In order to optimize the problem solution, an in-house parallel algorithm in CUDA-C language was developed to solve the problem in a Graphical Process Unity (GPU). A modify Successive Over-Relaxation (SOR-M) scheme was applied to minimizing the computational time. The thermal fields are analyzed to determine if the thermite generation heat is enough to create the plug. The study found that high-power thermite is required to make the P&A process. The study also found that a coupling between the cracks in the cement at high-temperature, liquid dolomite, and the mix of the liquid steel duct, and thermite are responsible to break the cement and create a plug to perform the P&A operation.

Copyright © 2020 ASMEThe present work addresses the subsonic aerodynamic coefficients model for bluff ellipsoidal hulls at transitional and turbulent Reynolds number. The drag, lift, and moment aerodynamic coefficients model are based on computational fluid dynamics (CFD) simulations for four bluff ellipsoids with aspect ratio of 1, 2, 3, and 4, in the Reynolds number range of 1×103 to 2×106 and angle of attack range from 0 to 20 degrees. The Large Eddy Simulation (LES) turbulence model is used with the sub-grid turbulence model Wall-Adapting Local-Eddy Viscosity (WALE) to solve the fluid field. To reduce computational simulation time, at a first instant, the mesh is gradually refined until the point that it does not influence anymore in the final result (mesh independence). For each aerodynamic coefficient a nonlinear equation structure, valid for all the ellipsoids, is proposed as a parametric model with parameters estimated using the least mean square algorithm applied to the results of the computational fluid dynamics simulations. The proposed equations have a superior performance, in terms of precision and number of terms, when compared to polynomial equations fitted to the same data.

© MDPI AG. All rights reserved.A thermal analysis of a 5 kVA dry-type transformer under linear and non-linear loads conditions is studied in this paper. The main goal here is to calculate the hottest-spot transformer temperature under free convection through the resolution of the heat conduction equation in three dimensions (3D) using COMSOL Multiphysics®. The proposed technique was validated through experimental data obtained in laboratory. The temperature inside the cores was measured under the influence of free convection. The radiation emission was also measured through a thermal camera. The heat transfer coefficient for both conditions was obtained from empirical correlations. The hottest-spot temperatures were determined from the analysis in the commercial software which was used for the numerical simulations of the transformer heating and cooling under some loading conditions. The temperature residuals, that is, the experimental temperature values subtracted by the numerical temperature values, were below 10%. The numerical analysis found that the hottest-spot temperatures in the core reached 20C above the transformer insulation limit. The location of the hottest-spot as well as the obtained temperatures can be used to improve more resistant dry-type transformers.

© 2018, Springer-Verlag London Ltd., part of Springer Nature.The determination of the thermal field in a turning process is fundamental to improve the process quality. Recently, the carbide tools have been coated with ceramic materials that present insulating characteristics. This work presents an analysis of the thermal effects of coating in a carbide tool during a turning process using the COMSOL® software and a nonlinear inverse problem. The thermal model consists of a coated carbide tool, a tool holder, and a shim represented by the transient three-dimensional heat diffusion equation with heat loss by convection and radiation. The heat flux, previously unknown, is obtained through the function specification method. In order to validate the methodology, the heat flux is compared with the author’s previous work. Titanium nitride (TiN) and aluminum oxide (Al2O3) are utilized as the coating materials. Both coatings present the expected behavior when less heat is dissipated to the cutting tool substrate. The coated carbide tools present higher temperatures than the uncoated carbide tool in the contact area. The study also found that the thicker the coating, the higher the temperature in the contact area. The results presented in this work may help the development of new long-lasting coated carbide tools.

© 2018 Elsevier Masson SASThis works proposes an Inverse methodology to estimate the thermal efficiency of a Gas Tungsten Arch welding (GTAW) process as a time-dependent function. The direct model consists in solving the non-linear three-dimensional heat diffusion equation through the Finite Difference Method in a C++ code. As the inverse methodology, the Golden Section optimization technique was used together with the Time Travelling Regularization to estimate the applied heat rate in the GTAW process. The Time Travelling Regularization was used to reduce the noise on the estimated heat input. Furthermore, a numerical Temperature moving sensor is proposed to determine the heat input as a time-dependent function. The methodology was applied in lab-controlled experiments based on a Robust Project matrix. The numerical analysis revealed that the thermal efficiency decreased as the arch torch moves. The proposed methodology also presented a higher sensitivity than the usual methods for the heat rate estimation and is a cheaper way to determine the melting efficiency in welding processes.

© 2018 Elsevier LtdThe heat flux inverse analysis is significantly affected by the heat flux distribution in laser welding simulation. This work proposed a different approach for the heat distribution which predicts the temperature and the weld bead in laser welding. The influence of the heat flux distribution in an inverse heat conduction problem applied on laser welding simulation is studied by comparing different heat distribution models. An inverse heat conduction algorithm based on the three-dimensional (3D) heat diffusion equation and the enthalpy function to model the phase change problem are used to estimate the heat flux under different heat distributions. The Time Traveling Regularization is applied with the Golden Section method to estimate the heat flux in the studied cases. The proposed cubic root and square root of the volumetric heat distribution presented a good agreement between the weld profile and the experimental temperatures. The heat rate estimation proves to be dependent on the heat distribution. The proposed methodology is an alternative to predict the weld bead profile and the thermal efficiency in low penetration laser welding.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland.This work presents a technique called Time Traveling Regularization (TTR) applied to an optimization technique in order to solve ill-posed problems. This new methodology does not interfere in the minimization technique process. The Golden Section method together with TTR are applied only to the objective function which will be minimized. It consists of finding an ideal timeline that minimizes an objective function in a defined future time step. In order to apply the proposed methodology, inverse heat conduction problems were studied. Controlled experiments were performed on 5052 aluminum and AISI 304 stainless steel samples to validate the proposed technique. One-dimensional and three-dimensional heat input experiments were carried out for the 5052 aluminum and AISI 304 stainless steel samples, respectively. The Sequential Function Specification Method (SFSM) was also used to be compared with the results of heat flux obtained by TTR. The estimated heat flux presented a good agreement when compared with experimental values and those estimated by SFSM. Moreover, TTR presented lower residuals than the SFSM.

© Emerald Publishing Limited.Purpose - The purpose of this article is the determination of the temperature fields in a weld region has always been an obstacle to the improvement of welding processes. As an alternative, the use of inverse problems to determine the heat flux during the welding process allows an analysis of these processes. Design/methodology/approach - This paper studies an alternative for the thermal analysis of the tungsten inert gas welding process on a 6,060 T5 aluminum alloy. For this purpose, a C++ code was developed, based on a transient three-dimensional heat transfer model. To estimate the amount of heat delivered to the plate, the specification function technique was used. Lab experiments were carried out to validate the methodology. A different experimental methodology is proposed to estimate the emissivity (radiation coefficient). Findings - The maximum difference between experimental and numerical temperatures is lower than 5 per cent. The determined emissivity value for the aluminum 6,060 T5 presented a good agreement with literature values. The thermal fields were analyzed as function of the positive polarity. The specification function method proved to be an adequate tool for heat input estimation in welding analysis. Originality/value - The proposed methodology proves to be a cheaper way to estimate the heat flux on the sample. The estimated power curves for the welding process are presented. The methodology to calculate the emissivity (radiation coefficient) was validated.

© 2017 by the authors.This work presents an analysis of the thermal influence of the heat transfer by convection and radiation during GTA (gas tungsten arc) welding process. The authors' in-house C++ previously-developed code was modified to calculate the amount of heat transfer by convection and radiation. In this software, an iterative Broydon-Fletcher-Goldfarb-Shanno (BFGS) inverse method was applied to estimate the amount of heat delivered to the plate when the appropriate sensitivity criteria were defined. The methodology was validated by accomplishing lab-controlled experiments on stainless steel AISI 304L and aluminum 6065 T5 plates. Due to some experimental singularities, the forced thermal convection induced by the electromagnetic field and thermal-capillary force were disregarded. Significant examples of these singularities are the relatively small weld bead when compared to the sample size and the reduced time of the welding process. In order to evaluate the local Nusselt number, empirical correlations for flat plates were used. The thermal emission was a dominant cooling effect on the aluminum cooling. However, it did not present the same behavior as the stainless steel samples. The study found that the heat losses by convection and radiation of the weld pool do not affect the cooling process significantly.

© 2016 Elsevier Ltd. All rights reserved.Numerical software based on the tridimensional diffusion equation with a moving source, a phase change and heat flux estimation by the non-linear interactive Broydon-Fletcher-Goldfarb-Shanno (BFGS) inverse technique was used to study the heat affected zone (HAZ) in GTA aluminum 6065 T5 alloy welding. GTA welding experiments were performed using thin aluminum plates in four t+ experimental conditions. In previous studies, the authors determined that the peak temperature tends to increase as the positive polarity becomes higher. To confirm this behavior, the samples were cut on the welded region and later characterized using an optical microscope (OM) and a scanning electronic microscope (SEM). The heating and cooling rates, determined from an in-house code, were compared with the microstructures and the grain size of the HAZ found in the samples. The results revealed a linear correlation between the grain size on the HAZ and the positive polarity. The study also showed that a significant change in the microstructure occurs during the process while the GTAW torch is still turned on. After the welding, when the GTAW torch was turned off, the cooling rate was the same for all welded zones, which indicates that the microstructural changes had already occurred.

© 2015 Elsevier Ltd.This work presents an alternative approach for the thermal analysis of the GTA (Gas Tungsten Arc) welding process on a 6065 T5 aluminum alloy. For this purpose, a C++ code was developed, based on a transient three-dimensional heat transfer model with phase change and mobile heat source. The thermal model took into account the dependence of thermal properties on temperature and heat losses by convection and radiation. The convection heat transfer coefficient and the emissivity were also considered variables with the temperature. To estimate the amount of heat delivered to the plate, the BFGS (Broydon-Fletcher-Goldfarb-Shanno) technique was used. Moreover, an analysis of the duration time of the electrode in positive (. t+) and negative (. t-) polarities was carried out. The methodology was validated by accomplishing lab controlled experiments. The aluminum samples lay on four conical head screws and submitted to a heat flux on one surface by the GTAW process torch. The torch displaces along the sample, thus simulating a real process. The numerical results presented low deviation when compared to the experimental results, which in turn, confirm the validation of the methodology for the study of the welding process presented.