Turbulence is described by the Spalart–Allmaras model and the thermal energy transport by an advection–diffusion model. The flow is predicted by the Reynolds Averaged Navier–Stokes equations. The level set functions are discretized by higher-order B-splines. The design domain is immersed into a background mesh and the geometry of fluid/solid interfaces is defined implicitly by one or multiple level set functions.

This analysis approach is integrated into a level set-based optimization framework. To address this challenge, this work investigates for the first time the use of an eXtended Finite Element Method (XFEM) approach to predict the physical responses of conjugate heat transfer problems considering turbulent flow. As heat is transferred at fluid/solid interfaces, it is crucial to accurately resolve the geometry and the physics responses across these interfaces. Heat exchange between fluid and solid can be enhanced by optimizing the system layout and the shape of the flow channels. The results represent excellent agreement with available analytical, numerical and experimental observations in the literature.Solving conjugate heat transfer design problems is relevant for various engineering applications requiring efficient thermal management. The accuracy and robustness of the proposed method are examined by several numerical examples for stationary and propagating crack problems in 2D and 3D settings. All implementational aspects and suggested remedies for the treatment of enriched elements, framework setup, evaluation of stress intensity factors, and numerical integration are described in detail. The model pre-processing, level set update, stress intensity factor calculation and crack propagation analysis are conducted by employing COMSOL's built-in features in conjunction with external MATLAB functions through COMSOL LiveLink. The Linear Elastic Fracture Mechanics (LEFM) is exclusively adopted for the crack analysis. To this end, for each set of enrichment functions, an additional Solid Mechanics module is incorporated into the numerical framework, coupled with compatible modifications to the internal variables.

An enrichment strategy is proposed, consistent with the structure of the software. This paper presents the first time implementation of the eXtended Finite Element Method (XFEM) in the general purpose commercial software COMSOL Multiphysics.

Comsol Xfem