High-power laser processing shows increasing importance in the manufacturing industry. Solid-state lasers provide optical powers of several kilowatts in continuous-wave mode with power densities of more than 1 MW/mm2, thus helping to achieve economically relevant processing speeds. However, to minimize health risks due to intense laser radiation, sophisticated safety concepts are required. An essential part of these concepts is the laser-process housing, which typically consists of metallic walls as passive shielding against laser radiation. The standard EN 60825-4 defines requirements and testing conditions for these shielding materials. Here, it is considered that the material durability depends not only on the laser irradiance on the material surface but also on the laser-spot size, which is attributed to hindered heat conduction at the spot edge due to heat accumulation occurring at larger spot sizes. However, this behavior has not been fully understood. In this work, a simplified finite-element modeling approach based on the heat equation is used to simulate the dependence of the material durability on the laser-spot size for 2 mm thick structural steel, a typical shielding material in industry. The calculated times to reach the material-melting temperature are compared with the measured material lifetimes upon laser irradiation. It is shown that the presented finite-element modeling can reproduce the general size dependence of the material durability. Thus, this analysis to calculate the times up to the material-melting start can be used to derive lower limits of the material lifetimes under defined irradiation conditions, suitable for designing the shielding sufficiently.
In this article, we develop a reduced basis method for efficiently solving the coupled Stokes/Darcy equations with parametric internal geometry. To accommodate possible changes in topology, we define the Stokes and Darcy domains implicitly via a phase-field indicator function. In our reduced order model, we approximate the parameter-dependent phase-field function with a discrete empirical interpolation method (DEIM) that enables affine decomposition of the associated linear and bilinear forms. In addition, we introduce a modification of DEIM that leads to non-negativity preserving approximations, thus guaranteeing positive-semidefiniteness of the system matrix. We also present a strategy for determining the required number of DEIM modes for a given number of reduced basis functions. We couple reduced basis functions on neighboring patches to enable the efficient simulation of large-scale problems that consist of repetitive subdomains. We apply our reduced basis framework to efficiently solve the inverse problem of characterizing the subsurface damage state of a complete in-situ leach mining site.
In this article, we develop a reduced basis method for efficiently solving the coupled Stokes/Darcy equations with parametric internal geometry. To accommodate the change in topology, we define the Stokes and Darcy domains implicitly via a phase-field indicator function. In our reduced order model, we approximate the parameter-dependent phase-field function with a discrete empirical interpolation method (DEIM) that enables affine decomposition of the associated linear and bilinear forms. In addition, we introduce a modification of DEIM that leads to positivity-preserving approximations, thus guaranteeing positive-definiteness of the system matrix. We also present a strategy for determining the required number of DEIM modes for a given number of reduced basis functions. We couple reduced basis functions on neighboring patches to enable the efficient simulation of large-scale problems that consist of repetitive subdomains. We apply our reduced basis framework to efficiently solve the inverse problem of characterizing the subsurface damage state of a complete in-situ leach mining site.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.