Hybrid integral transforms for flow development in ducts partially filled with porous media

• Autor(a) principal: Lisboa, Kleber Marques
• Data de Publicação: 2018
• Outros Autores: Cotta, Renato Machado
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRJ
• Texto Completo: http://hdl.handle.net/11422/8285
• topic: Single Domain Formulation; Channel Flow; Navier–Stokes equations; Integral Transforms; Porous Media; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS

A hybrid numerical–analytical solution is developed for laminar flow development in a parallel plate duct partially filled with porous media. The integral transform method is employed in combination with a single domain reformulation strategy for representing the heterogeneous media within the channel. A novel eigenfunction expansion basis is proposed, including abrupt spatial variations of physical properties due to the domain transitions. The introduction of the new basis allows for a solution with similar convergence rates as in previous applications with simpler formulations, as demonstrated through a careful convergence analysis of the expansions. The inherent automatic error control characteristic of the integral transforms approach then provides benchmark results for the developing velocity profile. Moreover, a physical analysis further verifies the consistency of both the proposed expansion and the mixed symbolic–numerical code developed. A detailed verification with a finite-element commercial code is also performed.