https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2019JB017482

Origin of Shallow Volcanic Tremor: The Dynamics of Gas Pockets Trapped Beneath Thin Permeable Media

Porous media’s porosity value is commonly taken as a constant for a given granular texture free from any type of imposed loads. Although such definition holds for those media at hydrostatic equilibrium, it might not be hydrodynamically true for media subjected to the flow of fluids. This article casts light on an alternative vision describing porosity as a function of fluid velocity, though the media’s solid skeleton does not undergo any changes and remain essentially intact. Carefully planned laboratory experiments support such as hypothesis and may help reducing reported disagreements between observed and actual behaviors of nonlinear flow regimes. Findings indicate that the so-called Stephenson relationship that enables estimating actual flow velocity is a case that holds true only for the Darcian conditions. In order to investigate the relationship, an accurate permeability should be measured. An alternative relationship, therefore, has been proposed to estimate actual pore flow velocity. On the other hand, with introducing the novel concept of effective porosity, that should be determined not only based on geotechnical parameters, but also it has to be regarded as a function of the flow regime. Such a porosity may be affected by the flow regime through variations in the effective pore volume and effective shape factor. In a numerical justification of findings, it is shown that unsatisfactory results, obtained from nonlinear mathematical models of unsteady flow, may be due to unreliable porosity estimates.

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Conceptual definition of porosity function for coarse granular porous media with fixed texture

Although extensive researches have been conducted in the analytical and numerical analysis of flow through rockfill structures, one of the main issues in these analyses which still needs attention is uncertainty quantification In this research, first, it was investigated and shown that the nature and source of uncertainty in rockfill hydraulic parameters can be different indicating random and fuzzy parameters Then, uncertainty analysis of gradually varied flow computations in rockfill structures was conducted using proposed hybrid and transformation methods in order to quantify the uncertainty in computed water surface profiles resulting from uncertainty in the model hydraulic parameters Although the proposed methods can be applied to any equation that quantifies the head loss in flow through rockfill structures, two commonly used equations, ie, Stephenson and Wilkins equations, were used in this study The methods were applied to a laboratory-scale physical model, and the numerical results were compared with the corresponding measured water surface levels Three main conclusions drawn from this study were: (1) the results of the two different uncertainty analysis methods did not show significant differences, but the transformation method was rather simple and computationally efficient in comparison with the hybrid method, (2) for both Wilkins and Stephenson equations, the experimental data were within the 90% confidence intervals resulting from both uncertainty analysis methods and (3) the proposed approach and methodologies in this study can be used by hydraulic engineers in analysis and design of real-life rockfill structures

Development and Comparison of Two New Methods for Quantifying Uncertainty in Analysis of Flow Through Rockfill Structures

In this communication, the joint impacts of the process of melting as well as wedge angle entity on hydromagnetic hyperbolic tangent nanofluid flow owing to permeable wedge-shaped surface in the incidence of suspended nanoparticles along with radiation, Soret and Dufour numbers are scrutinized. The mathematical model which represents the system consists of a system of highly non-linear coupled partial differential equations. These equations are solved using a finite-difference-based MATLAB solver which implements the Lobatto IIIa collocation formula and is fourth-order accurate. Further, the comparison of computed results is carried out with the previously reported articles and outstanding conformity is recorded. Emerged physical entities affecting the bearings of tangent hyperbolic MHD nanofluid velocity, distribution of temperature, and concentration of nanoparticles are visualized in graphs. In another line, shearing stress, the surface gradient of heat transfer, and volumetric rate of concentration are recorded in tabular form. Most interestingly, momentum boundary layer thickness and thicknesses of thermal as well as solutal boundary layers enhance with an increment of Weissenberg number. Moreover, an increment on tangent hyperbolic nanofluid velocity and decrement on the thickness of momentum boundary layer is visualized for the increment of numerical values of power-law index entity, which can determine the behavior of shear-thinning fluids.This study has applications for coating materials used in chemical engineering, such as strong paints, aerosol manufacturing, and thermal treatment of water-soluble solutions. 

https://www.nature.com/articles/s41598-023-30656-2.pdf

Numerical exploration of forced convection hydromagnetic hyperbolic tangent nanofluid flow over a permeable wedge with melting heat transfer

Abstract This discussion examines the combined effects of Brownian motion, radiation, Thermophorises, activation energy, suspended nanoparticles on hydromagnetic flow Williamson nanofluid produced by the melting process. In order to mathematically describe the system, a set of strongly non-linear coupled PDEs is used. A BVP4C MATLAB solver is used to resolve these equations. In addition, calculated findings are compared with previously published publications, and high levels of consistency are noted. The emerging Williamson MHD nanofluid sketches are graphically shown. Besides, tabular data on shear stress, heat transfer coefficient, and concentration is shown. Intriguingly, it can be shown that when the Williamson parameter increases, the momentum boundary layer corpulence decreases, while the thermal and solutal boundary layers corpulence increases. This research applies to chemical engineering coating materials such strong paints and aerosol manufacture. 

Simulation of Hydromagnetic Williamson nanofluid flow with melting heat transfer and Activation Energy across a porous exponential stretching surface

This paper aims to cast light on the coefficients of non-linear equation governing unsteady turbulent flow through coarse porous media commonly known as Forchheimer’s equation. Experimental pilot made use of a physical model consisting of a flume of 13 m length, being controlled by an electro-mechanical device to create different types of flow regimes. A range of granular media with a mean diameter of 7.5 mm for Small crashed (Sc) to 14 mm for Medium crashed (Mc) were packed in the flume at different runs to simulate coarse porous media capable of sustaining turbulent flow, either unsteady or steady. Findings indicate that: coefficient of the linear flow term decreases (47.3% and 91.9% in Sc and Mc aggregate) with increasing mean grain size, respectively. In addition, coefficient of the turbulent term-the effects of inertia forces-increases (87.9% and 27.2% in Sc and Mc aggregate) with increasing mean grain size, respectively. Furthermore, coefficient of the unsteady term-local acceleration term in the Forchheimer’s equationshows a rapid increase (146.9% in Sc and 125.6% in Mc) with increasing velocity. Moreover, the nature of hydraulic gradient (i) variations versus Reynolds number (Re) — which were plotted for all sets of observations-confirms the existence of turbulent conditions in most experiments. Finally, the head losses and contribution of above-mentioned terms to the pressure drop was quite analyzed.

Morteza Shokri

Papers

Experimental study of unsteady turbulent flow coefficients through granular porous media and their contribution to the energy losses

Conceptual definition of porosity function for coarse granular porous media with fixed texture