Viscous transport in eroding porous media

Chiu, Shang-Huan; Moore, Nicholas J.; Quaife, Bryan

doi:10.1017/jfm.2020.228

Cited by 22 publications

(21 citation statements)

References 87 publications

(194 reference statements)

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“…Transpiring wall porosity (β) is one of the vital structural parameters affecting the flow resistance of transpiration water. 16,27 Internal resistance coefficient (η) and permeability (ζ) are two significant factors to characterize the flow resistance above, 28 and can be obtained via the Darcy's law 22 and basic formulas of fluid flow. Internal resistance coefficient and permeabilities at various porosities conditions can be seen in Table 2.…”

Section: Influence Of Transpiring Wall Porositymentioning

confidence: 99%

“…Apparently, turbulent mixing and high-temperature reaction zones approached the reactor top inlet, and subcritical salt-dissolving zone expanded as transpiring wall porosity increased. This can be explained by the fact that increasing transpiring wall porosity decreased internal resistance coefficient but increased permeability 28 (see Table 2), and thereby transpiration water can diffuse more easily through the transpiring wall. As a result, a larger subcritical salt-dissolving zone was formed in the middle and lower zones of the reactor.…”

Section: Influence Of Transpiring Wall Porositymentioning

confidence: 99%

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Effects of structural parameters on water film properties of transpiring wall reactor

Feng

Wang

et al. 2021

AIChE Journal

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Corrosion and salt deposition problems severely restrict the industrialization of supercritical water oxidation. Transpiring wall reactor can effectively weaken these two problems by a protective water film. In this work, methanol was selected as organic matter, and the influences of vital structural parameters on water film properties and organic matter removal were studied via numerical simulation. The results indicate that higher than 99% of methanol conversion could be obtained and hardly affected by transpiration water layer, transpiring wall porosity and inner diameter.Increasing layer and porosity reduced reactor center temperature, but inner diameter's influence was lower relatively. Water film temperature reduced but coverage rate raised as layer, porosity, and inner diameter increased. Notably, the whole reactor was in supercritical state and coverage rate was only approximately 85% in the case of one layer. Increasing reactor length affected slightly the volume of the upper supercritical zone but enlarged the subcritical zone.

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Section: Influence Of Transpiring Wall Porositymentioning

confidence: 99%

Section: Influence Of Transpiring Wall Porositymentioning

confidence: 99%

Effects of structural parameters on water film properties of transpiring wall reactor

Feng

Wang

et al. 2021

AIChE Journal

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“…Flow-induced erosion acts across a range of scales in the natural world, from massive geological structures sculpted by wind or water [1,28,20,32,19], to mesoscopic patterns formed by surface or internal flows [6,7,36], and down to granular and porous networks slowly disintegrating in groundwater flows [10,34,22,15,8,11,37]. The associated nonlinear feedback between changing shapes and the surrounding flows can imprint across all of these scales, affecting large-scale features as well as small-scale ones, such as the microstructure of porous materials.…”

Section: Introductionmentioning

confidence: 99%

How fluid-mechanical erosion creates anisotropic porous media

Moore¹,

Cherry²,

Chiu³

et al. 2022

Preprint

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Using a Cauchy integral formulation of the boundary integral equations, we simulate the erosion a porous medium comprised of up to 100 solid bodies embedded in a Stokes flow. The grains of the medium are resolved individually and erode under the action of surface shear stress. Through nonlinear feedback with the surrounding flow fields, microscopic changes in grain morphology give way to larger-scale features in the medium such as channelization. The Cauchy-integral formulation and associated quadrature formulas enable us to resolve dense configurations of nearly contacting bodies. We observe substantial anisotropy to develop over the course of erosion; that is, the configurations that result from erosion generally permit flow in the longitudinal direction more easily than in the transverse direction by up to a factor of six. These results suggest that the erosion of solid material from groundwater flows may contribute to previously observed anisotropy of natural porous media.

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“…Our choice in discretizing time, first, before treating the spatial quantities, is not a new idea. A well-known approach is Rothe's method [11,12] in which a finite difference approximation is used for time derivatives and an integral equation solver is developed for the resulting sequence of elliptic PDEs (see e.g., [13,14,15,16,17,18,19]). The earlier developments for successive convolution methods, such as [5], are quite similar to Rothe's method in the treatment of the time derivatives.…”

Section: Introductionmentioning

confidence: 99%

Parallel Algorithms for Successive Convolution

Christlieb¹,

Guthrey²,

Sands³

et al. 2020

Preprint

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The development of modern computing architectures with ever-increasing amounts of parallelism has allowed for the solution of previously intractable problems across a variety of scientific disciplines. Despite these advances, multiscale computing problems continue to pose an incredible challenge to modern architectures because they require resolving scales that often vary by orders of magnitude in both space and time. Such complications have led us to consider alternative discretizations for partial differential equations (PDEs) which use expansions involving integral operators to approximate spatial derivatives [1,2,3]. These constructions use explicit information within the integral terms, but treat boundary data implicitly, which contributes to the overall speed of the method. This approach is provably unconditionally stable for linear problems and stability has been demonstrated experimentally for nonlinear problems. Additionally, it is matrix-free in the sense that it is not necessary to invert linear systems and iteration is not required for nonlinear terms. Moreover, the scheme employs a fast summation algorithm that yields a method with a computational complexity of O(N ), where N is the number of mesh points along a coordinate direction. While much work has been done to explore the theory behind these methods, their practicality in large scale computing environments is a largely unexplored topic. In this work, we explore the performance of these methods by developing a domain decomposition algorithm suitable for distributed memory systems along with shared memory algorithms. As a first pass, we derive an artificial Courant-Friedrichs-Lewy (CFL) condition that enforces a nearest-neighbor (N-N) communication pattern and briefly discuss possible generalizations. We also analyze several approaches for implementing the parallel algorithms by optimizing predominant loop structures and maximizing data reuse. Using a hybrid design that employs MPI and Kokkos [4] for the distributed and shared memory components of the algorithms, respectively, we show that our methods are efficient and can sustain an update rate > 1 × 10 8 DOF/node/s. We provide results that demonstrate the scalability and versatility of our algorithms using several different PDE test problems, including a nonlinear example, which employs an adaptive time-stepping rule.

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Viscous transport in eroding porous media

Cited by 22 publications

References 87 publications

Effects of structural parameters on water film properties of transpiring wall reactor

Effects of structural parameters on water film properties of transpiring wall reactor

How fluid-mechanical erosion creates anisotropic porous media

Parallel Algorithms for Successive Convolution

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