Search results

The purpose of this paper is to present an immersed volume method that accounts for solid conductive bodies (hat‐shaped disk) in calculation of time‐dependent, three‐dimensional, conjugate heat transfer and fluid flow.

The incompressible Navier‐Stokes equations and the heat transfer equations are discretized using a stabilized finite element method. The interface of the immersed disk is defined and rendered by the zero isovalues of a level set function. This signed distance function allows turning different thermal properties of each component into homogeneous parameters and it is coupled to a direct anisotropic mesh adaptation process enhancing the interface representation. A monolithic approach is used to solve a single set of equations for both fluid and solid with different thermal properties.

In the proposed immersion technique, only a single grid for both air and solid is considered, thus, only one equation with different thermal properties is solved. The sharp discontinuity of the material properties was captured by an anisotropic refined solid‐fluid interface. The robustness of the method to compute the flow and heat transfer with large materials properties differences is demonstrated using stabilized finite element formulations. Results are assessed by comparing the predictions with the experimental data.

The proposed method demonstrates the capability of the model to simulate an unsteady three‐dimensional heat transfer flow of natural convection, conduction and radiation in a cubic enclosure with the presence of a conduction body. A previous knowledge of the heat transfer coefficients between the disk and the fluid is no longer required. The heat exchange at the interface is solved and dealt with naturally.

Numerical modelling and simulation of metal forming is rapidly gaining prominence in many industries all over the world due to its effective saving of production time, effort and economy. In order to meet this need a special finite element code FORGE2 has been developed at CEMEF. In this work the theoretical basis of the FORGE2 along with its features such as thermo‐viscoplastic coupling, material compressibility and automatic mesh regeneration is reviewed and an attempt is made to simulate a few industrial forming processes taking into account the complex friction phenomena and thermal environment.

This paper presents the results of the simulation of the forging of a connecting rod. The calculation has been carried out by the code FORGE3 developed at the CEMEF laboratory. FORGE3 is a three‐dimensional finite element computer program that can simulate hot forging of industrial parts. The flow problem is solved using a thermomechanical analysis. The mechanical resolution and the thermal one are coupled by the way of the consistency K which is thermodependent, the plastic deformation in the volume of the material and the friction heat flux on the surface. The material behaviour is assumed to be incompressible and viscoplastic (Norton—Hoff law) with the associated friction law. The thermal resolution includes the case of non‐linear physical properties and boundary conditions. An explicit Euler scheme is used for the mechanical resolution and two‐step schemes for the thermal one. For the computation of other parameters, it is necessary to have a good approximation for the strain rate tensor. The Orkisz method has been used to determine the deviatoric stress tensor and p is calculated by an original smoothing method. The results show that it is possible to get good information on the flow and on the physical properties during forging of automotive parts. Comparisons have been made with experimental measurements with a reasonably good agreement.

The finite element analysis of deformation of viscoplastic material involves contact between the tool and the workpiece. Here unilateral contact condition with the possibility of nodes originally in contact, losing contact subsequently, is analysed in non‐steady state forming processes. Friction has been taken into consideration through a potential function. Node to node contact is analysed and contact forces at the node are used to decide if the node is to be released. Two different algorithms are presented for treating the nodal contact condition. The one step explicit method with projections on the surface of contact was already implemented in the FORGE2^® software. An implicit scheme is proposed and compared with the existing scheme. The advantages of this scheme are numerically shown by solving some examples. It is observed that the volume losses are reduced. This makes it possible to use larger time steps or increase the computational accuracy.

This paper aims to develop a robust set of advanced numerical tools to simulate multiphase flows under the superimposition of external uniform magnetic fields.

The flow has been simulated in a fully Eulerian framework by a {\it variational multi-scale} method, which allows to take into account the small-scale turbulence without explicitly model it. The multi-fluid problem has been solved through the convectively re-initialized level-set method to robustly deal with high density and viscosity ratio between the phases and the surface tension has been modelled implicitly in the level-set framework. The interaction with the magnetic field has been modelled through the classic induction equation for 2D problems and the time step computation is based on the electromagnetic interaction to guarantee convergence of the method. Anisotropic mesh adaptation is then used to adapt the mesh to the main problem’s variables and to reach good accuracy with a small number of degrees of freedom. Finally, the variational multiscale method leads to a natural stabilization of the finite elements algorithm, preventing numerical spurious oscillations in the solution of Navier–Stokes equations (fluid mechanics) and the transport equation (level-set convection).

The methodology has been validated, and it is shown to produce accurate results also with a low number of degrees of freedom. The physical effect of the external magnetic field on the multiphase flow has been analysed.

The dam-break benchmark case has been extended to include magnetically constrained flows.

The paper seeks to present an original method for the numerical treatment of thermal shocks in non‐linear heat transfer finite element analysis.

The 3D finite element thermal analysis using linear standard tetrahedral elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe ways to directly discourage the use of these elements. This is especially true in the case of solidification problems, in which melted alloys at very high temperature contact low diffusive mould materials. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M‐matrix form, which ensures an oscillation‐free solution.

The proposed “diffusion‐split” method consists basically of using a modified conductivity matrix. It allows for solutions based on linear tetrahedral elements. The performance of the method is evaluated by means of a test case with analytical solution, as well as an industrial application, for which a well‐behaved numerical solution is available.

The proposed method should be helpful for computational engineers and software developers in the field of heat transfer analysis. It can be implemented in most existing finite element codes with minimal effort.

The premise of this research is that the coupling of reinforcement learning algorithms and computational dynamics can be used to design efficient control strategies and to improve the cooling of hot components by quenching, a process that is classically carried out based on professional experience and trial-error methods. Feasibility and relevance are assessed on various 2-D numerical experiments involving boiling problems simulated by a phase change model. The purpose of this study is then to integrate reinforcement learning with boiling modeling involving phase change to optimize the cooling process during quenching.

The proposed approach couples two state-of-the-art in-house models: a single-step proximal policy optimization (PPO) deep reinforcement learning (DRL) algorithm (for data-driven selection of control parameters) and an in-house stabilized finite elements environment combining variational multi-scale (VMS) modeling of the governing equations, immerse volume method and multi-component anisotropic mesh adaptation (to compute the numerical reward used by the DRL agent to learn), that simulates boiling after a phase change model formulated after pseudo-compressible Navier–Stokes and heat equations.

Relevance of the proposed methodology is illustrated by controlling natural convection in a closed cavity with aspect ratio 4:1, for which DRL alleviates the flow-induced enhancement of heat transfer by approximately 20%. Regarding quenching applications, the DRL algorithm finds optimal insertion angles that adequately homogenize the temperature distribution in both simple and complex 2-D workpiece geometries, and improve over simpler trial-and-error strategies classically used in the quenching industry.

To the best of the authors’ knowledge, this constitutes the first attempt to achieve DRL-based control of complex heat and mass transfer processes involving boiling. The obtained results have important implications for the quenching cooling flows widely used to achieve the desired microstructure and material properties of steel, and for which differential cooling in various zones of the quenched component will yield irregular residual stresses that can affect the serviceability of critical machinery in sensitive industries.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

This paper sets out to show the feasibility of the genetic algorithm inverse method for the determination of the parameters of crystallization kinetics laws in isothermal and non‐isothermal conditions, using multiple experiments.

The mathematical model for crystallization kinetics determination and the numerical methods of its resolution are introduced. Crystallization kinetic parameters determined by approximate physical analysis and the inverse genetic algorithm method are presented. Injection molding simulations taking into account crystallization are performed using the finite element method.

It is necessary to perform the optimization on two parameters, transformed volume fraction and number of spherulites to obtain correct results. It is possible to use results from different samples, in spite of the dispersion of some values.

Experimental data for isothermal and non‐isothermal conditions were used and obtained good results for the parameters of crystallization kinetics laws from which the evolutions of overall crystallization kinetics and crystalline microstructure were deduced. Nevertheless, the dispersion of the experimental data concerning the number of spherulites obtained with different samples is important. The evolution of the number of spherulites is required for the optimization to get correct results.

An important result of this work is that the genetic algorithm optimization can be applied to this problem where the experiments cannot be performed with a single sample and the experimental data for the number of spherulites have low precision. Even if only the crystallization kinetics was considered, the feasibility in molding simulation has been shown.

Simulation of crystallization in injection molding is very important for a later prediction of the end‐use properties.

The purpose of this paper is to develop a finite volume approach for the simulation of three-dimensional two-phase (polymer melt and air) flow in plastic injection molding which is capable of robustly handling the mesh non-orthogonality and the discontinuities in fluid properties.

The presented numerical method is based on a cell-centered unstructured finite volume discretization with a volume-of-fluid technique for interface capturing. The over-relaxed approach is adopted to handle the non-orthogonality involved in the discretization of the face normal derivatives to enhance the robustness of the solutions on non-orthogonal meshes. A novel interpolation method for the face pressure is derived to address the numerical stability issues resulting from the density and viscosity discontinuities at the melt–air interface. Various test cases are conducted to evaluate the proposed method.

The presented method was shown to be satisfactorily accurate by comparing simulations with analytical and experimental results. Besides, the effectiveness of the proposed face pressure interpolation method was verified by numerical examples of a two-phase flow problem with various density and viscosity ratios. The proposed method was also successfully applied to the simulation of a practical filling case.

The proposed finite volume approach is more tolerant of non-orthogonal meshes and the discontinuities in fluid properties for two-phase flow simulation; therefore, it is valuable for engineers in engineering computations.