We analyze the sensitivity to image defects of the processing algorithm proposed by Salgado Sánchez et al. (Microgravity Sci. Technol. 37, 12, 2025) to evaluate melting bridge experiments in the context of the MarPCM microgravity project (Porter et al., Acta Astronaut. 210, 212–223, 2023). The algorithm uses the projection of input images onto the first m singular vectors (modes), obtained via Singular Value Decomposition (SVD), of the original (non-defective) image database. The resulting set of m amplitudes is then used as input for an Artificial Neural Network (ANN) that is trained to give the corresponding liquid fraction as an output. For the analysis presented here, the images are modified to generate a new database that includes rotated images, which represent optical misalignment, overexposed and underexposed images, which represent incorrect exposure time and/or aperture settings in the camera, noisy images and gappy images, which model the presence of dead pixels, bubbles and large reflections that compromise certain regions of the image. The results suggest that only relatively large defects are a concern for processing the experiment and that the most critical case is that of gappy images. Data repair algorithms based on SVD can be used to correct the defective images and reconstruct the missing information, which then allows for accurate processing.

Both Singular Value Decomposition (SVD) and Artificial Neural Networks (ANNs) can be powerful tools for image processing. Here they are applied in the context of the “Effect of Marangoni Convection on Heat Transfer in Phase Change Materials” (MarPCM) microgravity experiment [Porter et al. (Acta Astronautica 210, 212–223, 2023)], which investigates the use of thermocapillary (Marangoni) convection to expedite melting of organic Phase Change Materials (PCMs) in cuboidal and cylindrical domains. The processing of the cylindrical “melting bridge” experimental images is particularly challenging due to the converging lens effect caused by the curved interface and the refractive index of the liquid PCM. A combination of SVD and ANNs is used to propose an algorithm to process these images. The network is trained on a set of synthetic images of the melting bridge, generated via ray-tracing [Martinez et al. (Advances in Space Research 72, 1915–1928, 2023)] then projected onto the eigenmodes associated with the largest singular values of the image database, which includes snapshots of the melting process in all representative cases. Two optimal algorithm architectures are described, characterized by the number of SVD modes considered in the projection and the hyperparameters of the ANN. The performance of the algorithm is analyzed in terms of its ability to associate images with the correct liquid fraction. The processing strategy is tested by applying it to images obtained from ground experiments using the scientific prototype of the MarPCM cuboidal cell.

A quantitative phase-field model has been developed to simulate aqueous corrosion on low carbon steel under chloride-based electrolytes at different pHs. All relevant transport phenomena are included through physically interpretable variables. In particular, both diffusion and migration charge transport are modelled. Separated electrical potentials for the electrolyte and the metal are considered, and physically meaningful boundary conditions are provided. Using this model, different polarization conditions can be predicted and many parameters not observable/challenging during experiments, can be obtained. Finally, since the proposed model includes different time scales, a segregated numerical integration algorithm is proposed to speed up simulations.

Efficient and precise optimisation methodologies, when applied to improve the real performance of engineering devices, must balance the need to reduce high computational cost and maintain accuracy in the treatment of first principles and physicochemical properties. This is the aim of the time– and parameter–adaptive model order reduction technique presented in this article. In contrast to (standard) pre–processed reduced order models (ROMs), the proposed adaptive strategy presents two principal advantages: (i) it does not require any previous information to derive an accurate ROM, which provides a substantial acceleration of solution calculations, and (ii) the periods of full order model calculations can be further reduced when information needed by the optimisation algorithms to derive ROM updates is provided by the previous simulations. Its implementation within the framework of efficient gradient–like optimisation methods requires a careful analysis of the sensitivities computation in order to resolve certain issues inherent to adaptive ROMs. The proposed technique is applied to the optimisation of the performance of a three–dimensional lithium–ion cell described by the electrochemical pseudo–four–dimensional battery model (p4D model). In particular, the results obtained when maximising the energy delivered by a graphite–NMC811 cell and a graphite–LFP cell demonstrate the robustness and efficacy of the method. The presented methodology has been implemented in a software tool named OptiBat, developed in the framework of a H2020 project, and available in the project website https://defacto-project.eu/defacto-rom-optimisation-tool/.

The air-drying of resin impregnated paper sheets in industrial lines, formed by a serial array of furnaces, presents a high number of different controllable operational parameters whose adjustment, usually done by the maintenance staff, leads to non-efficient configurations. A model-based numerical tool, which predicts accurately in a few seconds the evolution of the paper temperature and paper grammage along the line for a given combination of the input operational parameters (direct design), was used coupled to an optimization tool to select appropriate operational parameters (inverse design) that ensure a drying process quality (i.e., fulfills an objective grammage profile) with a minimum of energy consumption. The numerical tool was capable of selecting suitable configurations with an energy reduction of up to 50% for several tested industrial cases, making the model an essential tool in the framework of the increasingly relevant role of digital twins in industry.

A time-adaptive reduced order model (ROM) is developed for the electrochemical model for lithium-ion cells derived by Doyle, Fuller, and Newman (DFN) [M. Doyle, T. F. Fuller and J. Newman, J. Electrochem. Soc. , 140 1526 (1993)]. The main advantage of a time-adaptive strategy is that it does not require a set of full order model simulations to be generated beforehand and, thus, it is the most cost-effective alternative when no databases are available. However, the reduction of this electrochemical problem exhibits special features that require ad hoc solutions, preventing the application of generic strategies. This complexity is carefully analysed, focusing on mode selection, treatment of non-linearities and error estimation. Despite of all this analysis being done for a pseudo-two-dimensional DFN model, we show that such complexity is intrinsic to the physics of the electrochemical problem, making the analysis applicable to a pseudo-four-dimensional DFN model, where results prove that the benefits of a reduction in the number of degrees of freedom are more self-evident. The efficiency, robustness and accuracy of our method are remarkable, as shown by the macroscopic (cell voltage) and internal (variable distributions) results obtained from the simulation of two different electrochemical cells under several charge/discharge C-rates.

battery; cell manufacturing; cell ageing; workflow; multiscale models; multiphysics models

A new electrolyte transport parameter identification methodology, based on the numerical solution of a symmetric Li-Li cell model, is presented. In contrast to available techniques in the literature, where small concentration perturbations are generated in testing setups and linearization is assumed to identify transport properties for the initial salt concentration, large currents are used here to excite nonlinear dynamics able to reveal concentration dependent transport properties. This approach allows a significant reduction in the experimental effort. The proposed methodology is applied to two synthetic experiments. Firstly, an ideal case (where all difficulties associated to stripping and plating dynamics on Li metal surface are neglected) is considered in order to show both the details of the proposed methodology and its performance (specially its robustness, including the effect of the noise level in the voltage measurements in the experiment). A second case considers the effect of complex stripping and plating dynamics to show that, provided (macroscopic) modelling/identification of this dynamics is carried out, the proposed methodology is still able to accurately identify electrolyte transport properties using a simple experimental test setup.

Dimensionless analysis arises as an appropriate methodology to study battery cells behavior since it brings the opportunity to identify limiting mechanisms in the battery cell performance by analysing a reduced number of dimensionless parameters. These parameters are obtained by condensating the physical dimensional parameters involved in the description of the electrochemical phenomena taking place in the cell. Here, based on the well known Doyle, Fuller and Newman model [M. Doyle, T.F. Fuller, J. Newman, J. Electrochem. Soc., 140(6) 1526-1533 (1993)] (DFN model, in short), a comprehensive set of dimensionless parameters is derived and the information arising from each dimensionless parameter is explained. Application to the design of a solid polymer electrolyte cell is considered, where limiting transport mechanisms are identified through dimensionless parameters analysis and guidelines for a cell redesign are also drawn from this analysis. Predictions made by inspection of the derived comprehensive set of dimensionless parameters are validated both numerically (using the DFN model) and experimentally.

Industrial drying lines of resin-impregnated paper are formed by contiguous furnaces where hot air jets impinge on the surface of the moving paper sheet. The number of production parameters that conditions the process is very high, making the final drying prediction, and the optimal adjustment of the production parameters, very complex tasks. A novel numerical tool for the fast prediction of this industrial drying is presented. The model, obtained from local mass and energy equations for the paper sheet, and fed with results from three-dimensional computational fluid dynamic simulations and thermo-gravimetric tests, determines the evolution of the paper weight along the line for any given combination of production parameters: paper velocity, furnaces air temperatures and mass flows, among others. The model is validated in an industrial line with 11 furnaces, 2 impregnation stages, and more than 150 adjustable operational input parameters, leading to relative errors in the predicted paper temperature evolution and final paper weight of less than 7% and 1%, respectively. Likewise, the model coupling with an optimization tool is also presented to show its capabilities on selecting the best production parameters for prescribed conditions, making the model a useful tool in the framework of the increasingly relevant role of mathematical models in industry.

The number of operational variables that determines the cooling process of steel wire, given by the conveyor velocity and the different fan sections powers (controlled independently), lead to a dependency of the cooling on a high multidimensional parameter space whose potential combinations are impossible to be analyzed, either experimentally or by numerical simulation of a thermal–metallurgical model. To tackle this problem, an efficient strategy, based on the use of Higher Order Singular Value Decomposition (HOSVD), is presented. The approach presented provides a Reduced-Order Model (ROM) capable of predicting quite accurately the cooling curve for any combination of the process parameters. Fast online predictions of the cooling rates allow to incorporate accurate modeling results in many Engineering tools, such as model predictive control algorithms or plant simulation software. Also, the ROM in combination with an optimization tool finds the adequate operational parameters with significant reduction of energy consumption.

This article presents an experimental and numerical study on the heat transfer behavior in the channel flow past a confined rectangular cylinder at (relatively) low Reynolds number. The work is motivated by a previous article by the authors (Meis et al. (2010)) that illustrated through a 2D numerical model that a significant heat transfer improvement can be achieved for some particular configurations of the cylinder (suggesting an interesting guideline for the design of micro channel heat exchangers). The objective of the present study was to make a comparison between the results of the actual experimental tests (using a setup as close as possible to a practical micro heat exchanger device) and the previous numerical results of the 2D simplified model, and to understand the differences. The experimental setup consisted of a rectangular cross section channel in which a cylinder with rectangular cross section was placed. The blockage ratio was 2:1, and the channel aspect ratio in the span-wise direction was 17:1. A heated aluminum block in the stream-wise direction was inserted in the lower channel wall right downstream of the rectangular cylinder. A mechanical device was implemented to allow the rectangular cylinder to be inclined at will with respect to the incoming flow. A stagnation chamber, representative of an actual practical engineering situation, was placed upstream of the channel entrance. Three different flow Reynolds numbers (Re) based on twice the channel cross-section height (the channel hydraulic diameter) were tested: 200, 400, and 600. The Nusselt number (Nu) was measured as a function of Re and the rectangular cylinder inclination angle. Regarding the results obtained, it was found that the hysteretic heat transfer behavior that was present in some previous 2D simulations and was responsible for a remarkable heat transfer enhancement did not appear in the experimental tests. This difference can be ascribed to the fact that idealized inflow boundary conditions were used in the 2D computations while an actual stagnation chamber with finite dimensions was used in the experiments. This is corroborated by 3D numerical simulations of the experimental setup, showing that heat transfer enhancement (relative to a parallel channel flow) is associated with vorticiy generated in the stagnation chamber. In addition, 3D numerical simulations showed that further modifications in the stagnation chamber design did not change significantly these results. Finally, obvious as it may seem, it is worth highlighting that micro channel heat exchanger design guidelines based on 2D models should be considered with much care, since flow in realistic configurations can be dominated by effects associated to the overall device design. (C) 2018 Elsevier Ltd. All rights reserved.

To educate in Industrial Mathematics is one of the main objectives of ECMI. In the past editions of the ECMI conferences the different training opportunities offered by institutions have been analyzed.

Mechanical properties of industrial manufactured wire rod depend on the chemical composition of the steel and the air-cooling rates underwent by the product after hot rolling, generated by fans located beneath a conveyor. The number of operational variables that determines the cooling process, given by the conveyor velocity and the different fan sections powers (controlled independently), lead to a dependency of the cooling on a high multidimensional parameter space whose potential combinations are impossible to be analyzed, either experimentally or by numerical simulation of a thermal-metallurgical model. To tackle this problem, an efficient strategy, based on the use of Higher Order Singular Value Decomposition (HOSVD), is presented. This approach consists firstly in the prediction of the cooling rate using numerical simulation of a thermal-metallurgical model for a reduced number of points of the parameter space and therefore the generation of a database with these simulated cases. Then, the HOSVD technique is applied to provide simplified global descriptions of the multidimensional database that, finally, permits to predict quite accurately the cooling curve for any combination of the process parameters. The work presented shows a robust and simple strategy on the selection of (a reduce number of) particular combinations of process parameters that are used to construct the full database. Fast on-line predictions of the cooling rates (once the database has been built) allow to incorporate accurate modelling results in many Engineering tools, such as model predictive control algorithms or plant simulation software.

Although programs have been developed for the design of tools for hot forging, its design is still largely based on the experience of the tool maker. This obliges to build some test matrices and correct their errors to minimize distortions in the forged piece. This phase prior to mass production consumes time and material resources, which makes the final product more expensive. The forging tools are usually constituted by various parts made of different grades of steel, which in turn have different mechanical properties and therefore suffer different degrees of strain. Furthermore, the tools used in the hot forging are exposed to a thermal field that also induces strain or stress based on the degree of confinement of the piece. Therefore, the mechanical behaviour of the assembly is determined by the contact between the different pieces. The numerical simulation allows to analyse different configurations and anticipate possible defects before tool making, thus, reducing the costs of this preliminary phase. In order to improve the dimensional quality of the manufactured parts, the work presented here focuses on the application of a numerical model to a hot forging manufacturing process in order to predict the areas of the forging die subjected to large deformations. The thermo-mechanical model developed and implemented with free software (Code-Aster) includes the strains of thermal origin, strains during forge impact and contact effects. The numerical results are validated with experimental measurements in a tooling set that produces forged crankshafts for the automotive industry. The numerical results show good agreement with the experimental tests. Thereby, a very useful tool for the design of tooling sets for hot forging is achieved.

Modern industrial aircraft design requires a large amount of sufficiently accurate aerodynamic and aeroelastic simulations. Current computational fluid dynamics (CFD) solvers with aeroelastic capabilities, such as the NASA URANS unstructured solver FUN3D, require very large computational resources. Since a very large amount of simulation is necessary, the CFD cost is just unaffordable in an industrial production environment and must be significantly reduced. Thus, a more inexpensive, yet sufficiently precise solver is strongly needed. An opportunity to approach this goal could follow some recent results (Terragni and Vega 2014 SIAM J. Appl. Dyn. Syst. 13 330–65; Rapun et al 2015 Int. J. Numer. Meth. Eng. 104 844–68) on an adaptive reduced order model that combines ‘on the fly’ a standard numerical solver (to compute some representative snapshots), proper orthogonal decomposition (POD) (to extract modes from the snapshots), Galerkin projection (onto the set of POD modes), and several additional ingredients such as projecting the equations using a limited amount of points and fairly generic mode libraries. When applied to the complex Ginzburg–Landau equation, the method produces acceleration factors (comparing with standard numerical solvers) of the order of 20 and 300 in one and two space dimensions, respectively. Unfortunately, the extension of the method to unsteady, compressible flows around deformable geometries requires new approaches to deal with deformable meshes, high-Reynolds numbers, and compressibility. A first step in this direction is presented considering the unsteady compressible, two-dimensional flow around an oscillating airfoil using a CFD solver in a rigidly moving mesh. POD on the Fly gives results whose accuracy is comparable to that of the CFD solver used to compute the snapshots.

SummaryA reduced order model (ROM) is presented for the long‐term calculation of subsurface oil/water flows. As in several previous ROMs in the field, the Newton iterations in the full model (FM) equations, which are implicit in time, are projected onto a set of modes obtained by applying proper orthogonal decomposition (POD) to a set of snapshots computed by the FM itself. The novelty of the present ROM is that the POD modes are (i) first calculated from snapshots computed by the FM in a short initial stage, and then (ii) updated on the fly along the simulation itself, using new sets of snapshots computed by the FM in even shorter additional runs. Thus, the POD modes adapt themselves to the local dynamics along the simulation, instead of being completely calculated at the outset, which requires a computationally expensive preprocess. This strategy is robust and computationally efficient, which is tested in 10‐ and 30‐year simulations for a realistic reservoir model taken from the SAIGUP project. Copyright © 2016 John Wiley & Sons, Ltd.

Wire rod of steel, produced by a hot rolling process, is cooled on a conveyor by action of fans sited under it. Mechanical properties of rod depend on chemical composition of steel and cooling rate experimented by the product. A mathematical model is developed in order to predict the thermal and metallurgical evolution of the steel rod on the conveyor. Convection and radiation losses are considered and the influence of the laying head is also discussed. Simulation results are compared with experimental measures obtained by an optical pyrometer in a real industrial process. Several product diameters and fan configurations are analyzed. Conclusions about the good accuracy of the model are shown. Thanks to the short computational time that the developed tool takes to predict the temperature of the wire rod along the conveyor, the tool can be potentially used in an on-line control system for the cooling process of wire rods.

A fully-coupled model of quenching by submerging for steel workpieces is presented. The model includes cooling of the piece due to piece-to-bath heat transfer calculations by solving the multiphase problem of an evaporable fluid, as well as the corresponding metallurgical transformations, the generation of residual stresses and associated geometrical distortions. The heat transfer model takes into account different boiling stages, from film boiling at very high workpiece surface temperatures, to single-phase convection at surface temperatures below saturation. The evolution and activation of each heat transfer mechanism depend on the dynamics of the vapor-liquid multiphase system of the quenching bath. The multiphase flow was modeled using the drift-flux mixture model, including an equation of conservation of energy of the liquid phase. Metallurgical transformations, geometrical distortions and residual stresses at the end of the process, are obtained based on the different cooling rates along the piece. The final distribution of metallurgical phases is obtained by the integration of the thermal evolution and using information of the CCT diagrams of studied steels. The analysis of deformations and residual stresses takes into account elasto-plasticity (without viscosity effects), transformation induced plasticity and hardening restoring phenomena. Comparison of results considering the approach presented here versus a simplified heat transfer model indicates that the level of induced residual stresses are noticeable different implying the necessity of developing a more precise heat transfer quenching model.