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In this paper, we report a novel symmetry-breaking phenomenon that occurs in turbulent convective flow in periodic porous media in the intermediate porosity flow regime for values of porosities in between 0.8 and 0.9. Large eddy simulation is used to numerically simulate the momentum and thermal transport inside the porous medium at the microscale level. The phenomenon is observed to occur for periodically repeating porous media consisting of an in-line arrangement of circular cylinder solid obstacles, such as typically found in heat exchangers. The transition from symmetric to asymmetric flow occurs in between the pore scale Reynolds numbers of 37 (laminar) and 100 (turbulent), and asymmetric flow patterns are reported for Reynolds numbers up to 1,000. A Hopf bifurcation resulting in unsteady oscillatory laminar flow marks the origin of a secondary flow instability arising from the interaction of the shear layers around the solid obstacle. In turbulent flow, stochastic phase difference in the vortex wake oscillations caused by the secondary flow instability results in asymmetrical velocity and temperature distributions in the pore space. Consequently, high and low velocity flow channels are formed in the pore space that leads to the asymmetrical velocity and pressure distributions. At the macroscale level, symmetry-breaking results in residual transverse drag force components acting on the solid obstacle surfaces. The vortex wake oscillations caused by the secondary flow instability promote attached flow on the solid obstacle surface, which improves the surface averaged heat flux from the solid obstacle surface. 

The role of solid obstacle surface roughness in turbulent convection in porous media is not well understood, even though it is frequently used for heat transfer enhancement in many applications. The focus of this paper is to systematically study the influence of solid obstacle surface roughness in porous media on the microscale flow physics and report its effect on macroscale drag and Nusselt number. The Reynolds-averaged flow field is numerically simulated using the realizable k-ε model for a flow through a periodic porous medium consisting of an in-line arrangement of square cylinders with square roughness particles on the cylinder surface. Two flow regimes are identified with respect to the surface roughness particle height—fine and coarse roughness regimes. The effect of the roughness particles in the fine roughness regime is limited to the near-wall boundary layer around the solid obstacle surface. In the coarse roughness regime, the roughness particles modify the microscale flow field in the entire pore space of the porous medium. In the fine roughness regime, the heat transfer from the rough solid obstacles to the fluid inside the porous medium is less than that from a smooth solid obstacle. In the coarse roughness regime, there is an enhancement in the heat transfer from the rough solid obstacle to the fluid inside the porous medium. Total drag reduction is also observed in the fine roughness regime for the smallest roughness particle height. The surface roughness particle spacing determines the fractional area of the solid obstacle surface covered by recirculating, reattached, and stagnating flow. As the roughness particle spacing increases, there are two competing factors for the heat transfer rate—increase due to more surface area covered by reattached flow and decrease due to fewer roughness particles on the solid obstacle surface. Decreasing the porosity and increasing the Reynolds number amplify the effect of the surface roughness on the microscale flow. The results suggest that heat transfer in porous media can be enhanced, if the increase in drag can be overcome. The results also show that the fine roughness regime, which is frequently encountered due to corrosion, is detrimental to the heat transfer performance of porous media. 

Developing the next generation of cellular therapies will depend on fast, versatile, and efficient cellular reprogramming. Novel biomaterials will play a central role in this process by providing scaffolding and bioactive signals that shape cell fate and function. Previously, our lab reported that dry macroporous alginate scaffolds mediate retroviral transduction of primary T cells with efficiencies that rival the gold-standard clinical spinoculation procedures, which involve centrifugation on Retronectin-coated plates. This scaffold transduction required the scaffolds to be both macroporous and dry. Transduction by dry, macroporous scaffolds, termed “Drydux transduction,” provides a fast and inexpensive method for transducing cells for cellular therapy, including for the production of CAR T cells. In this study, we investigate the mechanism of action by which Drydux transduction works through exploring the impact of pore size, stiffness, viral concentration, and absorption speed on transduction efficiency. We report that Drydux scaffolds with macropores ranging from 50–230 μm and with Young's moduli ranging from 25–620 kPa all effectively transduce primary T cells, suggesting that these parameters are not central to the mechanism of action, but also demonstrating that Drydux scaffolds can be tuned without losing functionality. Increasing viral concentrations led to significantly higher transduction efficiencies, demonstrating that increased cell–virus interaction is necessary for optimal transduction. Finally, we discovered that the rate with which the cell–virus solution is absorbed into the scaffold is closely correlated to viral transduction efficiency, with faster absorption producing significantly higher transduction. A computational model of liquid flow through porous media validates this finding by showing that increased fluid flow substantially increases collisions between virus particles and cells in a porous scaffold. Taken together, we conclude that the rate of liquid flow through the scaffolds, rather than pore size or stiffness, serves as a central regulator for efficient Drydux transduction. 

The focus of this paper is a numerical simulation study of the flow dynamics in a periodic porous medium to analyse the physics of a symmetry-breaking phenomenon, which causes a deviation in the direction of the macroscale flow from that of the applied pressure gradient. The phenomenon is prominent in the range of porosity from 0.43 to 0.72 for circular solid obstacles. It is the result of the flow instabilities formed when the surface forces on the solid obstacles compete with the inertial force of the fluid flow in the turbulent regime. We report the origin and mechanism of the symmetry-breaking phenomenon in periodic porous media. Large-eddy simulation (LES) is used to simulate turbulent flow in a homogeneous porous medium consisting of a periodic, square lattice arrangement of cylindrical solid obstacles. Direct numerical simulation is used to simulate the transient stages during symmetry breakdown and also to validate the LES method. Quantitative and qualitative observations are made from the following approaches: (1) macroscale momentum budget and (2) two- and three-dimensional flow visualization. The phenomenon draws its roots from the amplification of a flow instability that emerges from the vortex shedding process. The symmetry-breaking phenomenon is a pitchfork bifurcation that can exhibit multiple modes depending on the local vortex shedding process. The phenomenon is observed to be sensitive to the porosity, solid obstacle shape and Reynolds number. It is a source of macroscale turbulence anisotropy in porous media for symmetric solid-obstacle geometries. In the macroscale, the principal axis of the Reynolds stress tensor is not aligned with any of the geometric axes of symmetry, nor with the direction of flow. Thus, symmetry breaking in porous media involves unresolved flow physics that should be taken into consideration while modelling flow inhomogeneity in the macroscale. 

The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$ , is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. ( J. Fluid Mech , vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$ ) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a ‘two-length-scale diffusion’ model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$ . In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations. 

Turbulence modeling in porous media can be greatly improved by combining high-resolution numerical methods with modern data-driven techniques. The development of accurate macroscale models (length scale greater than the pore size) will enable real-time systemic simulations of porous media flow. We consider the case of turbulent flow in homogeneous porous media, typically encountered in engineered porous media (heat exchangers, metamaterials, combustors, etc.). The underlying microscale flow field is inhomogeneous and determined by the geometry of the porous medium. Neural Networks are able to resolve the geometry-dependence and the non-linearity of porous media turbulent flow. We are proposing to separate the macroscale model into individual blocks that predict a unique aspect of the microscale flow, such as microscale spatial flow distribution and vortex dynamics. In the present work, we determine the feasibility of the prediction of the Reynolds-averaged microscale flow patterns by using Convolutional Neural Networks (CNN). The porous medium is represented by using a square lattice arrangement of circular cylinder solid obstacles. The pore-scale Reynolds number of the flow is 300. The porosity of the porous medium is varied from 0.45 to 0.92 with 60 steps. The microscale flow field is simulated by using Large Eddy Simulation (LES) with a compact sixth-order finite difference method. We demonstrate satisfactory prediction of the microscale flow field using the CNN with a global error less than 10%. We vary the number of training samples to study the deterioration of the model accuracy. The CNN model offers a O(106) speedup over LES with only 10% loss in accuracy. 

The influence of microscale flow structures (smaller than the pore size) on turbulent heat transfer in porous media has not been yet investigated. The goal of this study is to determine the influence of the micro-vortices on convection heat transfer in turbulent porous media flow. Turbulent flow in a homogeneous porous medium was investigated using Large Eddy Simulation (LES) at a Reynolds number of 300. We observed that the convection heat transfer characteristics are dependent on whether the micro-vortices are attached or detached from the surface of the obstacle. There is a spectral correlation between the Nusselt number and the pressure instabilities due to vortex shedding. A secondary flow instability occurs due to high pressure regions forming periodically near the converging pathway between obstacles. This causes local adverse pressure gradient, affecting the flow velocity and convection heat transfer. This study has been performed for obstacles with shapes of square and circular cylinders at porosities of 0.50 and 0.87. Understanding the dominant modes that affect convection heat transfer can aid in finding an optimum geometry for the porous medium.