Vademecum-based GFEM (V-GFEM): optimal enrichment for transient problems

This is the accepted version of the following article: [Canales, D., Leygue, A., Chinesta, F., González, D., Cueto, E., Feulvarch, E., Bergheau, J. -M., and Huerta, A. (2016) Vademecum-based GFEM (V-GFEM): optimal enrichment for transient problems. Int. J. Numer. Meth. Engng, 108: 971–989. doi: 10.1002/nme.5240.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5240/fullThis paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off-line and stored in memory in the form of a computational vademecum so that they can be used on-line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum-generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes.Peer ReviewedPostprint (author's final draft

Design for Additive Manufacturing of Conformal Cooling Channels Using Thermal-Fluid Topology Optimization and Application in Injection Molds

Additive manufacturing allows the fabrication parts and tools of high complexity. This capability challenges traditional guidelines in the design of conformal cooling systems in heat exchangers, injection molds, and other parts and tools. Innovative design methods, such as network-based approaches, lattice structures, and structural topology optimization have been used to generate complex and highly efficient cooling systems; however, methods that incorporate coupled thermal and fluid analysis remain scarce. This paper introduces a coupled thermal-fluid topology optimization algorithm for the design of conformal cooling channels. With this method, the channel position problem is replaced to a material distribution problem. The material distribution directly depends on the effect of flow resistance, heat conduction, as well as forced and natural convection. The problem is formulated based on a coupling of Navier-Stokes equations and convection-diffusion equation. The problem is solved by gradient-based optimization after analytical sensitivity derived using the adjoint method. The algorithm leads a two -dimensional conceptual design having optimal heat transfer and balanced flow. The conceptual design is converted to three-dimensional channels and mapped to a morphological surface conformal to the injected part. The method is applied to design an optimal conformal cooling for a real three dimensional injection mold. The feasibility of the final designs is verified through simulations. The final designs can be exported as both three-dimensional graphic and surface mesh CAD format, bringing the manufacture department the convenience to run the tool path for final fitting

User defined nodal displacement of numerical mesh for analysis of screw machines in FLUENT

Growing demands to reduce energy consumption are driving researchers towards in-depth analysis of positive displacement machines. Twin screw compressors are amongst the most common types of positive displacement machines. These machines have inherently complex geometry due to intricate rotor profiles used. As the details of the internal flows are difficult to obtain experimentally, Computational Fluid Dynamics (CFD) offers a good alternative for evaluation of internal flow patterns. However, implementation of CFD is challenging due complex deforming geometries. In this paper, a customised grid generator SCORGTM developed by authors is used to generate numerical meshes for commercially available solver ANSYS FLUENT. FLUENT is an unstructured solver which offers flexibility of using both segregated and coupled solution algorithms. Segregated algorithms are generally faster which results in shorter product development time. Interface with FLUENT is implemented by performing User Defined Nodal Displacements (UDND) of grids generated by SCORG in a parallel framework. For this purpose, SCORG and UDND are coupled and extended to work with FLUENT's parallel architecture. The developed code is compiled within the solver. The oil free air screw compressor with 'N' profile rotors and 3/5 lobe combination is modelled for 8000 RPM and 6000 RPM. Finally, the predicted performance values with FLUENT are compared to previously calculated CFX predictions and experimental results. FLUENT requires shorter solution time to obtain same accuracy of CFX

Grid Generation and CFD Analysis of Variable Geometry Screw Machines

This thesis describes the development of grid generation and numerical methods for predicting the flow in variable geometry, positive displacement screw machines. It has been shown, from a review of available literature, that the two main approaches available to generate deforming grids for the CFD analysis of 3D transient flow in screw machines are algebraic and differential. Grids that maintain the cell count and connectivity, during solution, provide the highest accuracy and customised grid generation tools have the capability to accommodate large mesh deformations. For the analysis of screw rotors with a variable lead or varying profile, these techniques are suitable but are required to be developed further with new procedures that can define the three dimensional variation of geometry of the rotors onto the computational grid. An algebraic grid generation method was used for deforming grid generation of variable lead and varying profile rotors. Functions were developed for correlating a specified lead variation along the rotor axis with the grid spacing. These can be used to build a continuously variable lead with linear, quadratic or higher order functions. For variable profile rotors, a novel approach has been developed for three dimensional grid structuring. This can be used to specify a continuously variable rotor profile, a variable lead, and both internal and external rotor engagement, thus making it possible to generate rotor domains with conical and variable lead geometries. New grid distribution techniques were developed to distribute boundary points on the rotors from the fixed points on the rack and the casing. These can refine the grid in the region of interlobe leakage gaps between the rotors, produce a one to one connected interface between them and improve the cell quality. Inflation layers were applied and tested for mesh refinement near the rotor boundaries. Case studies have been presented to validate the proposed grid generation techniques and the results have been compared with experimental data. Simulated results agreed well with measured data and highlighted the conditions where deviations are highest. Results with variable geometry rotors showed that they achieve steeper internal pressure rise and a larger discharge port area could be used. With variable lead rotors the volumetric efficiency could be improved by reducing the sealing line length in the high pressure zone. Calculations with inflation layers showed that local velocities were better predicted but there was no substantial influence on the integral performance parameters

International Workshop on Finite Elements for Microwave Engineering

When Courant prepared the text of his 1942 address to the American Mathematical Society for publication, he added a two-page Appendix to illustrate how the variational methods first described by Lord Rayleigh could be put to wider use in potential theory. Choosing piecewise-linear approximants on a set of triangles which he called elements, he dashed off a couple of two-dimensional examples and the finite element method was born. … Finite element activity in electrical engineering began in earnest about 1968-1969. A paper on waveguide analysis was published in Alta Frequenza in early 1969, giving the details of a finite element formulation of the classical hollow waveguide problem. It was followed by a rapid succession of papers on magnetic fields in saturable materials, dielectric loaded waveguides, and other well-known boundary value problems of electromagnetics. … In the decade of the eighties, finite element methods spread quickly. In several technical areas, they assumed a dominant role in field problems. P.P. Silvester, San Miniato (PI), Italy, 1992 Early in the nineties the International Workshop on Finite Elements for Microwave Engineering started. This volume contains the history of the Workshop and the Proceedings of the 13th edition, Florence (Italy), 2016 . The 14th Workshop will be in Cartagena (Colombia), 2018