Non-Darcian immiscible two-phase flow through porous materials (Darcy–Forchheimer–Brinkman Model)

• Published in: Thermal science and engineering progress Vol. 29; p. 101204
• Main Authors: Elkady, M.S., Abdelaziz, Gamal B., Sharshir, Swellam W., Mohamed, Abdelkarim Y.A., Elsaid, Ashraf Mimi, El-Said, Emad M.S., Mohamed, Salwa M., Abdelgaied, Mohamed, Kabeel, A.E.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2022
• Subjects: Heat transfer; Immiscible; Non-Darcian effects; Porosity variation; Two phase flow; Non-Darcian effects; Porosity variation; Two phase flow; Immiscible; Heat transfer
• ISSN: 2451-9049; 2451-9049
• DOI: 10.1016/j.tsep.2022.101204

•This study concerns Non-Darcian Immiscible Two-Phase Flow and Heat Transfer in Porous Materials considering (Darcy-Forchheimer–Brinkman Model)•The influence of inertia “Forschheimer term”, Porosity, gravity, and macroscopic shear “Brinkman term” are pointedly analyzed numerically with finite volume scheme.•Test section of a vertical, cylinder is filled with spherical beads and exposed to constant wall temperature. The two flowing fluids are assumed to move concurrently, downward, and steady with no variation in their properties along time and length.•Numerical Solution was compared with experimental results achieving good agreement. A macroscopic-scale Darcy's equation is applicable for both single-phase and multi-phase flow through classical porous materials with a porosity of 0–100% at a low Reynolds number. However, it has more than restrictions at high Reynolds number flow therefore, it cannot be applied in these conditions. The fundamental Darcy’s law assumes no inertial effect and friction between fluid and walls (channeling effect). In this research study, the influence of inertia “Forchheimer term” and macroscopic shear “Brinkman term” are pointedly considered. The influence of porosity and gravity parameters are also considered. Momentum equation considering viscous term, gravity, inertial term, and channeling effect for each phase beside energy equation are derived and solved by finite volume technique. Test section of a vertical, cylinder is filled with spherical beads and exposed to constant wall temperature. The two flowing fluids are assumed to move concurrently, downward, and steady with no variation in their properties along time and length. The numerical results are acquired for conditions of particle diameter to the pipe radius ratio 0.176 < D < 0.65, Reynolds number ranging 101 < Re < 106, saturation ranging 0 < S < 1, and dimensionless pressure gradient up to 1010. Numerical prediction based on this formulation have been depicted to fair agree the experimental data. The novelty of this study is utilizing a general wide model to express two-phase flow through porous media considering the influences of inertial force, Brinkman macroscopic shear friction, gravity, and porosity variation. The newly acquired findings are compared to the past studies by El-Kady (1997) and Poulikakos and Renken (1987) for single-phase flow through porous materials and satisfactory agreements are achieved.