Session K16: Porous Media Flows: Mixing and Turbulence (8:45am - 9:30am CST)

Elastic Turbulence is Spatially Patchy in 3-D Porous Media

Polymer additives can produce unstable flow fluctuations, often known as “elastic turbulence”. This unstable flow can be harnessed to aid the mobilization of trapped immiscible fluids from porous media for applications like enhanced oil recovery (EOR) and groundwater remediation. However, it remains unknown how elastic turbulence manifests in a disordered porous medium. Here, we provide the first direct visualization of elastic turbulence in a 3-D porous medium. Surprisingly, this unstable flow is not spatially homogenous, as is commonly assumed: instead, we observe discrete pore-scale pockets of unstable flow, giving rise to spatially patchy elastic turbulence throughout the medium. We demonstrate that the formation of these unstable pockets is determined by variations in the pore-scale geometry, as quantified by a dimensionless parameter that characterizes the persistence of elastic stresses in the flow. Guided by this finding, we directly link the energy dissipated by these pore-scale fluctuations to the flow resistance through the entire medium, enabling us to develop a general model by which macroscopic transport properties can be predicted. Our work thus provides a general framework by which elastic turbulence in porous media can be predicted and controlled.   

Numerical investigation of the non-stationary nature of turbulence in porous media

Microscale turbulence in porous media constitutes a new physical phenomenon that exhibits dual properties of both classical internal and external turbulent flows. The flow field consists of both swirling micro-vortices generated behind the solid obstacles and coherent eddies in the primary flow. There is a need to characterize the dynamics of these flow structures in order to understand how to model the resulting inhomogeneous flow field. We use LES to simulate turbulent flow in porous media, represented by a homogenous array of circular cylinder solid obstacles. We observe that the spatial two-point velocity auto-correlation function inside the porous medium shows correlation behind each solid obstacle in the vicinity of the micro-vortices. The statistical similarity suggests that vortex shedding in porous media with a periodic structure is not a wholly random process, but is characterized in part by a harmonic nature. Thus, the re-correlation behind each solid obstacle is an indication of non-stationarity of the flow. We vary the porosity and the Reynolds number to show that this flow behavior is repeatable.   

Effects of grain-scale sediment-bed roughness on surface-subsurface mass exchange

In aquatic environments such as rivers, the exchange of solutes across the interface between the sediment and the overlying water plays a significant role in controlling biogeochemical processes. Most previous studies on characterizing this exchange are focused on flows with sediment bedforms much larger than individual sediment grains. Detailed understanding of the effects of grain-scale bed roughness on the exchange is limited. Our recent pore-resolved simulations of interface turbulence (Shen, Yuan and Phanikumar, JFM, 2020, 892: A20) revealed that, even in the absence of bed form, the grain-scale roughness of a flat river bed may lead to significant mass flux into the sediment. Here, we quantify the important macroscopic exchange quantities such as the exchange flux, subsurface flow paths characteristics, and the residence-time distribution. Results show that (1) grain-scale bed roughness generates multiscale subsurface flow paths that reach scales much larger than the grain diameter and (2) the roughness-induced hyporheic storage is dependent on the roughness characteristics. These observations indicate that, despite its small scale, the bed roughness can induce significant hyporheic exchange similar to that induced by a larger-scale bedform.   

Stretching and Folding in Intermittent Two-Phase Porous Media Flows

Mixing in multiphase porous media flows is crucial to a wide range of processes taking place in the subsurface as well as in industrial and biological settings, including CO$_2$ sequestration, catalysts, and drug delivery. Here we investigate the effect of intermittent multiphase flow on fluid stretching and folding, a key mechanism driving solute mixing and reaction in porous media. We show that the addition of a second fluid phase and an intermittently propagating immiscible fluid-fluid interface induces chaotic flows, characterized by exponential stretching in the pore space. Using lattice Boltzmann simulations across a wide range of flow rates, we quantify the Lyapunov exponent (mean chaotic stretching rate) as a function of the capillary number. Exponential stretching is underpinned by folding events associated with the intermittent motion of the interface. The Lyapunov exponent is found to decay with increasing capillary number, implying that the increasing flow intermittency observed at lower capillary numbers increases the mixing efficiency. We propose a mechanistic model that allows linking the basic multiphase flow properties to the chaotic mixing rate, opening new perspectives to understand mixing and reaction in multiphase porous media flows.   

Particle resolved DNS study of turbulence effects on hyporheic mixing in randomly packed sediment beds

High-fidelity direct numerical simulations (DNS) are used to investigate the interactions between stream flow turbulence and groundwater flow through a porous sediment bed. The mixing between the surface water and groundwater occurs in the porous region beneath the streams, termed as the hyporheic zone. Permeability Reynolds number $Re_k$, which represents the ratio of sediment permeability length scale to the viscous length scale, is varied (2.56, 6.6 and 13.0) to understand its influence on hyporheic mixing at the sediment-water interface (SWI). Statistics of mean flow and turbulence are compared to the data from experimental setup of Voermans $\emph{et al.}$ (J. Fluid Mech., vol. 824, 2017, pp. 413-437). It is found that at the SWI, stream-wise and vertical turbulence intensities, form-induced vertical and shear stress increase with $Re_k$, consistent with the experimental data. The double averaged (DA) TKE budget is analyzed to quantify the relative importance of different terms in energy transport mechanisms. Eulerian two-point cross correlations are computed to investigate the influence of turbulence and fluctuating pressure on sweep and ejection motions near the SWI. The anisotropy distribution of Reynolds stress at SWI is studied to analyze the turbulence structures.