Regimes of flow through cylinder arrays subject to steady pressure gradients

• Published in: International journal of heat and mass transfer Vol. 159; p. 120072
• Main Authors: Khalifa, Zahra, Pocher, Liam, Tilton, Nils
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2020; Elsevier BV
• Subjects: Arrays; Chemical reactors; Circular cylinders; Computational fluid dynamics; Continuity equation; Cylinder arrays; Fluid flow; Fluid mechanics; Heat exchangers; Mathematical analysis; Mathematical models; Non-Darcy flow; Pore-scale simulations; Porosity; Porous media; Pressure gradients; Reynolds number; Steady flow; Stokes flow; Unit cell; Vortex shedding; Vortices; Cylinder arrays; Pore-scale simulations; Non-Darcy flow
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2020.120072

•Perform a thorough parametric study of the various pore-scale and macroscale flow regimes that occur in period cylinder arrays.•Solve the pore-scale Navier–Stokes equations using finite volume methods with immersed boundaries.•Vary porosity, Reynolds number, and cylinder arrangement, covering pore-scale Stokes flow to pore-scale vortex shedding.•Show how competing viscous, and inertial effects give rise to up to five macroscale flow regimes.•We find the practice of fitting Forchheimer-type equations to data from a wide range of Reynolds numbers produces conflicting results in the literature. Flows through periodic cylinder arrays have been studied extensively for applications to heat exchangers, porous media, chemical reactors, and computational fluid mechanics. Nevertheless, the variation of the pore and macro-scale flow-regimes with porosity, driving pressure gradient, and cylinder arrangement remains not fully explored. We consequently perform a thorough parametric study of such regimes for both inline and staggered arrays of circular cylinders. The Navier–Stokes and continuity equations are solved using finite-volume and immersed boundary methods. We vary the porosity from minimum values for which cylinders nearly touch, to values approaching unity. We vary the Reynolds number from values producing Stokes flow to those producing pore-scale vortex shedding. Using the results of over 1000 simulations, we explore how competition between viscous and inertial effects produces five macroscopic flow regimes. We document the validity limits of each regime, and explore how they impact the modelling of non-Darcy flow regimes. We find the practice of fitting Forchheimer-type equations to data from a wide range of Reynolds numbers produces conflicting results in the literature. For inline arrays, the Forchheimer regime is not always present, and has a smaller validity regime than alternative models. For staggered arrays, the Forchheimer regime has a strong presence, but care must be taken to account for the presence of two different Forchheimer-type regimes. We also show that transition to vortex shedding is sensitive to the numerical domain size, because the mode of instability need not be periodic over the same unit cell as the steady flow. This significantly complicates the study of vortex shedding.