Pore-scale numerical analysis of morphological characteristics and their influence on flow behavior in compressed virtual open-cell polyurethane foams

Abstract

This study presents a numerical investigation integrating morphological characterization and flow response analysis within a porous medium subjected to uniaxial compression. Two modeling approaches are explored: periodic cell structures and Voronoï-based stochastic models. These approaches are analyzed within the framework of XPHD (eX-Poro-Hydro-Dynamic) lubrication, which aims to replace traditional lubricants in turbomachinery guide and support systems with a more efficient and environmentally friendly alternative to minimize energy losses. Identifying optimal materials for XPHD applications presents several challenges due to the continuous interaction between the imbibing fluid and the porous structure under dynamic compression, leading to complex mechanical behaviors. Within this context, the ANR SOFITT project preliminarily identified open-cell polyurethane foams as potential candidates due to their extensive range of physical properties. This study focuses on developing a modeling methodology for open-cell foam structures, aiming to replicate the geometry of polyurethane foams to predict fluid flow behavior under specific XPHD operating conditions. This approach facilitates the evaluation of morphological parameter variations and their impact on key properties necessary for selecting the optimal material. For morphological characterization, tomographic images of polyurethane foam samples subjected to different compression rates are analyzed using the digital volume correlation (DVC) method. The extracted morphological parameters serve as a foundation for generating virtual foams, combining CAD-based modeling with morphological data to create periodic and Voronoï-based structures. For flow modeling, numerical simulations conducted using OpenFOAM are compared with experimental data acquired in a preliminary study. The flow profiles and permeability measurements derived from simulations exhibit strong agreement with experimental observations. Further analysis establishes a correlation between foam internal morphology and fluid flow behavior. Voronoï-based foams demonstrate permeability and tortuosity values closer to those of real foams compared to periodic cell structures, a difference attributed to their respective internal morphologies—random versus periodic. Periodic cell models tend to overestimate permeability due to their uniform ligament configurations, which limit flow disturbances. Additionally, the study examines the deformation mechanisms of virtual foams and their correlation with modeling techniques to assess their suitability for deformation modeling. The Forchheimer coefficient $C_f$ is systematically lower in virtual foams than in real foams, highlighting the reduced inertial effects induced by the simplified numerical structures. The increasing discrepancy in $C_f$ with higher compression rates confirms the influence of structural simplifications on fluid flow response.