Abstract
Direct numerical simulation based on incompressible Navier–Stokes equations with an immersed boundary method is used to simulate accelerating porous media flow through a bed of uniform spheres arranged in hexagonal close packing order. The transient flow is realised by driving initially resting fluid by a constant pressure gradient. A wide spectrum of Reynolds number based on the sphere diameter and volume-averaged velocity is considered, which ranges from creeping flow up to a Reynolds number of approximately 350, where turbulent flow structures are evident inside the pores. It is found that nonlinear dependence of the volume-averaged velocity with respect to the applied pressure gradient is the consequence of emergence of streamwise jets and the accompanying streamwise vortices, as previously observed for other sphere pack arrangements. Furthermore, two distinct flow modes are identified in the steady flow regime which satisfy full geometric symmetries. The flow then becomes unsteady around Reynolds number of 90 which coincides with a partial breaking of the symmetries, and pore-scale turbulence emerges once all the symmetries vanish when Reynolds number is larger than 200. For all the considered unsteady flow, independent of being turbulent or not, we observe a consistent sequence of flow structure evolution during the flow development with progressively broken symmetries albeit at widely varying instantaneous Reynolds numbers. Moreover, we show that the symmetry breaking takes place in larger pore spaces first, then propagate into smaller pores located in downstream.
Highlights
There are many real-world porous media flow problems that are transient rather than steady, for instance, flow through our respiratory system, a forest inside a developing atmospheric boundary layer, and wave-induced current inside a coral community (Lowe et al 2008; Rogers et al 2016)
Our main focus in this paper is the transient part for the porous media flow, first we discuss about the Reynolds number dependency of the steady-state superficial streamwise velocity
Steadystate is visibly achieved for all the simulations, we observe that the flow with Resteady ≥ 91 becomes unsteady, the values from the cases with above-threshold Reynolds number need to be treated with care
Summary
There are many real-world porous media flow problems that are transient rather than steady, for instance, flow through our respiratory system, a forest inside a developing atmospheric boundary layer, and wave-induced current inside a coral community (Lowe et al 2008; Rogers et al 2016). Turbulence and Combustion (2020) 105:581–606 on steady-state flow, with few exceptions such as Hill et al (2001a) who numerically studied transient ordered/random sphere-pack flow being accelerated from rest, only in the zero Reynolds number limit. The precise Reynolds number limits to distinguish those flow regimes vary greatly in the literature—possibly due to the diverse porous media geometries that were considered—and they remain topics of active research. To contribute to this aspect, we consider a porous medium consisting of uniform touching spheres packed in the well-defined arrangement called hexagonal closed packing (HCP).
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