Numerical Simulation of Density-Driven Flow and Heat Transport Processes in Porous Media Using the Network Method

Cánovas, Manuel; Alhama, Iván; García, Gonzalo; Trigueros, Emilio; Alhama, F.

doi:10.3390/en10091359

Cited by 12 publications

(6 citation statements)

References 27 publications

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“…Thus, the network method is a quite simple tool because the researcher must only be familiarized with a few rules of circuit theory (constitutive Ohm's law and Kirchhoff's theorems). The reliability of the proposed method has been demonstrated in many other engineering problems such as soil consolidation, tribology, elasticity, solute transport and heat transfer, among others (García-Ros et al, 2019;Marín et al, 2012;Morales et al, 2012;Cánovas et al, 2017;Cánovas et al, 2015).…”

Section: Ec 379mentioning

confidence: 93%

A different approach to the network method: continuity equation in flow through porous media under retaining structures

Martínez‐Moreno

García‐Ros

Alhama

2020

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Purpose This study aims to present a new numerical model for the simulation of water flow through porous media of anisotropic character, based on the network simulation method and with the use of the free code Ngspice. Design/methodology/approach For its design, it starts directly from the flow conservation equation, which presents several advantages in relation to the numerical simulation of the governing equation in terms of the potential head. The model provides very precise solutions of streamlines and potential patterns in all cases, with relatively small meshes and acceptable calculation times, both essential characteristics when developing a computational tool for engineering purposes. The model has been successfully verified with analytical results for non-penetrating dams in isotropic media. Findings Applications of the model are presented for the construction of the flow nets, calculation of uplift pressures, infiltrated flow and average exit gradient in anisotropic scenarios with penetrating dams with and without sheet piles, being all this output information part of the decision process in ground engineering problems involving these retaining structures. Originality/value This study presents, for the first time, a numerical network model for seepage problems that is not obtained from the Laplace's governing equation, but from the water flow conservation continuity equation.

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Section: Ec 379mentioning

confidence: 93%

A different approach to the network method: continuity equation in flow through porous media under retaining structures

Martínez‐Moreno

García‐Ros

Alhama

2020

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“…The network simulation method has been successfully employed in numerous fields of applied engineering, such as ceramic coatings [36], dispersion of atmospheric pollutants [37], reinforced concrete corrosion [38], soil consolidation [39,40], seepage [41], heat transport [42][43][44], and many physical problems in engineering [30]. This technique makes use of the powerful algorithms of the circuit resolution codes [32,33] that are able to successfully cope with coupled and strong non-linear mathematical models, including Gear s fixed time methods [45], trapezoidal integration [31], and iterative methods, such as Runge-Kutta.…”

Section: Introductionmentioning

confidence: 99%

A Network Model for Electroosmotic and Pressure-Driven Flow in Porous Microfluidic Channels

et al. 2022

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In this work, the network simulation method is presented as a tool for the numerical resolution of the electroosmotic and pressure-driven flow problem in microchannels with rectangular and cylindrical geometries. Based on the Brinkman equation for steady flow and constant porosity, the network model is designed using spatial discretization. An equivalent electrical circuit is obtained by establishing an analogy between the physical variable fluid velocity and electric potential. The network model is solved quickly and easily employing an electrical circuit resolution code, providing solutions for the velocity profile in the channel cross-section and the total circulating flow. After simulating two practical cases, the suitability of the grid is discussed, relating the relative errors made in the variables of interest with the number of cells used. Finally, two other applications, one for rectangular geometries and the other for cylindrical channels, show the effects the main parameters controlling the flow in these types of channels have on velocities and total flow: the zeta potential of the soil pores, applied potential and pressure gradients, and the boundary condition modified by the zeta potential in the walls of the channel.

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“…The method has two phases: (i) the elaboration of a network model (electrical circuit equivalent to the process) and (ii) the simulation of the problem (obtaining the results of the network model) by means of a suitable program that allows the resolution of electrical circuits [21,22]. Recently, this technique has been successfully used in the simulation of a wide variety of problems in different fields of engineering, such as electrochemistry [23,24], elasticity [25], heat transfer [26] and tribology [27], providing accurate solutions in all cases. Its versatility is so high that, provided the appropriate equivalences are established (geometric, of the model and its variables of interest), it could be applied in other fields of knowledge such as neural networks [28] or geometric modeling [29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Heat Transport Problems in Porous Media Coupled with Water Flow Using the Network Method

2021

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In the present work, a network model for the numerical resolution of the heat transport problem in porous media coupled with a water flow is presented. Starting from the governing equations, both for 1D and 2D geometries, an equivalent electrical circuit is obtained after their spatial discretization, so that each term or addend of the differential equation is represented by an electrical device: voltage source, capacitor, resistor or voltage-controlled current source. To make this possible, it is necessary to establish an analogy between the real physical variables of the problem and the electrical ones, that is: temperature of the medium and voltage at the nodes of the network model. The resolution of the electrical circuit, by means of the different circuit resolution codes available today, provides, in a fast, simple and precise way, the exact solution of the temperature field in the medium, which is usually represented by abaci with temperature-depth profiles. At the end of the article, a series of applications allow, on the one hand, to verify the precision of the numerical tool by comparison with existing analytical solutions and, on the other, to show the power of calculation and representation of solutions of the network models presented, both for problems in 1D domains, typical of scenarios with vertical flows, and for 2D scenarios with regional flow.

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Numerical Simulation of Density-Driven Flow and Heat Transport Processes in Porous Media Using the Network Method

Cited by 12 publications

References 27 publications

A different approach to the network method: continuity equation in flow through porous media under retaining structures

A different approach to the network method: continuity equation in flow through porous media under retaining structures

A Network Model for Electroosmotic and Pressure-Driven Flow in Porous Microfluidic Channels

Numerical Simulation of Heat Transport Problems in Porous Media Coupled with Water Flow Using the Network Method

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