A new interpolation technique to deal with fluid-porous media interfaces for topology optimization of heat transfer
| Autor: | Pierre-Henri Cocquet, Delphine Ramalingom, Alain Bastide |
|---|---|
| Přispěvatelé: | Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT (PIMENT), Université de La Réunion (UR) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Optimization problem
General Computer Science Discretization Continuous adjoint method 02 engineering and technology Interpolation function 01 natural sciences Physics::Fluid Dynamics 0203 mechanical engineering Sigmoid function Heat transfer Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Topology optimization [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] 0101 mathematics Boussinesq approximation (water waves) Mathematics Finite volume method Natural convection General Engineering Laminar flow 010101 applied mathematics 020303 mechanical engineering & transports [PHYS.MECA.THER]Physics [physics]/Mechanics [physics]/Thermics [physics.class-ph] Interpolation |
| Zdroj: | Computers and Fluids Computers and Fluids, Elsevier, 2018, ⟨10.1016/j.compfluid.2018.04.005⟩ |
| ISSN: | 0045-7930 |
| DOI: | 10.1016/j.compfluid.2018.04.005⟩ |
| Popis: | This paper proposes a new interpolation technique based on density approach to solve topology optimization problems for heat transfer. Natural convection forces are dominated as Richardson number is equal to 2.8. Problems are modeled under the assumptions of steady-state laminar flow using the incompressible Navier–Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. The governing equations are discretized using finite volume elements and topology optimization is performed using adjoint sensitivity analysis. Material distribution and effective conductivity are interpolated by two sigmoid functions respectively hτ(α) and kτ(α) in order to provide a continuous transition between the solid and the fluid domains. Comparison with standard interpolation function of the literature (RAMP function) shows a smaller transition zone between the fluid and the solid thereby, avoiding some regularization techniques. In order to validate the new method, numerical applications are investigated on some geometric configurations from the literature, namely the single pipe and the bend pipe. Lastly, as two new parameters are introduced thanks to the interpolation functions, we study their impact on results of the optimization problem. The study shows that the proposed technique is a viable approach for designing geometries and fluid-porous media interfaces are well-defined. |
| Databáze: | OpenAIRE |
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