scholarly journals Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 696
Author(s):  
Bekzodjon Fayziev ◽  
Gafurjan Ibragimov ◽  
Bakhtiyor Khuzhayorov ◽  
Idham Arif Alias
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Kinetic Equations ◽  
Sufficient Conditions ◽  
Computational Mathematics ◽  
Deposition Kinetics ◽  
Dynamic Factors ◽  
Suspension Filtration

Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.

scholarly journals A Deep Bed Filtration Model of Two-Component Suspension in Dual-Zone Porous Medium

2020 ◽  
Vol 10 (8) ◽  
pp. 2793
Author(s):  
Bakhtiyor Khuzhayorov ◽  
Bekzodjon Fayziev ◽  
Gafurjan Ibragimov ◽  
Norihan Md Arifin
Keyword(s):  
Porous Medium ◽  
Particle Deposition ◽  
Kinetic Equations ◽  
Suspended Particles ◽  
Model Parameters ◽  
Deposition Kinetics ◽  
Input Section ◽  
Two Component ◽  
Suspension Filtration ◽  
Moving Fluid

In the paper, a mathematical model for the filtration of two-component suspensions in a dual-zone porous medium is considered. The model consists of the mass balance equations, the kinetic equations for active and passive zones of porous medium for each component of the suspension and Darcy’s law. To solve the problem, a numerical algorithm for computer experimentation is developed on the basis of finite difference method. Based on numerical results, the main characteristics of suspension filtration in a porous medium are established. Influences of model parameters on transport and deposition of suspended particles of two-component suspension in porous media are analysed. It is shown that the polydispersity of suspension and multistage nature of the deposition kinetics can lead to various effects that are not characteristic for the transport of one-component suspensions with one-stage particle deposition kinetics. In particular, in distribution of the concentration of suspended particles in a moving fluid non-monotonic dynamics are obtained at individual points in the medium. It is shown that at the points of the medium near to the input section, the concentration of deposited particles can reach partial capacities in the passive zone.

Numerical Study on the Performance of a Tube With Inserted Porous Media of Various Thermal Conductivities

2016 ◽  
Author(s):  
Tariq Amin Khan ◽  
Wei Li
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Porous Media ◽  
Velocity Profile ◽  
Fluid Transport ◽  
Energy Transport ◽  
Numerical Study ◽  
Darcy Number ◽  
Local Thermal Equilibrium ◽  
Working Fluid

Numerical study is performed on the effect of thermal conductivity of porous media (k) on the Nusselt number (Nu) and performance evaluation criteria (PEC) of a tube. Two-dimensional axisymmetric forced laminar and fully developed flow is assumed. Porous medium partially inserted in the core of a tube is investigated under varied Darcy number (Da), i.e., 10−6 ≤ Da ≤ 10−2. The range of Re number used is 100 to 2000 and the conductivity of porous medium is 1.4 to 202.4 W/(m.K) with air as the working fluid. The momentum equations are used to describe the fluid flow in the clear region. The Darcy-Forchheimer-Brinkman model is adopted for the fluid transport in the porous region. The mathematical model for energy transport is based on the one equation model which assumes a local thermal equilibrium between the fluid and the solid phases. Results are different from the conventional thoughts that porous media of higher thermal conductivity can enhance the performance (PEC) of a tube. Due to partial porous media insertion, the upstream parabolic velocity profile is destroyed and the flow is redistributed to create a new fully develop velocity profile downstream. The length of this flow redistribution to a new developed laminar flow depends on the Da number and the hydrodynamic developing length increases with increasing Da number. Moreover, the temperature profile is also readjusted within the tube. The Nu and PEC numbers have a nonlinear trend with varying k. At very low Da number and at a lower k, the Nu number decreases with increasing Re number while at higher k, the Nu number first increases to reach its peak value and then decreases. At higher Re number, the results are independent of k. However, at a higher Da number, the Nu and PEC numbers significantly increases at low Re number while slightly increases at higher Re number. Hence, the change in Nu and PEC numbers neither increases monotonically with k, nor with Re number. Investigation of PEC number shows that at very low Da number (Da = 10−6), inserting porous media of a low k is effective at low Re number (Re ≤ 500) while at high Re number, using porous material is not effective for the overall performance of a tube. However, at a relatively higher Da number (Da = 10−2), high k can be effective at higher Re number. Moreover, it is found that the results are not very sensitive to the inertia term at lower Da number.

scholarly journals Numerical Study of the Effect of Magnetic Field on Nanofluid Heat Transfer in Metal Foam Environment

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hamid Shafiee ◽  
Elaheh NikzadehAbbasi ◽  
Majid Soltani
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Volume Fraction ◽  
Numerical Study ◽  
Computational Simulation ◽  
Thermodynamic Efficiency ◽  
Two Phase

The magnetic field can act as a suitable control parameter for heat transfer and fluid flow. It can also be used to maximize thermodynamic efficiency in a variety of fields. Nanofluids and porous media are common methods to increase heat transfer. In addition to improving heat transfer, porous media can increase pressure drop. This research is a computational simulation of the impacts of a magnetic field induced into a cylinder in a porous medium for a volume fraction of 0.2 water/Al2O3 nanofluid with a diameter of 10 μm inside the cylinder. For a wide variety of controlling parameters, simulations have been made. The fluid flow in the porous medium is explained using the Darcy-Brinkman-Forchheimer equation, and the nanofluid flow is represented utilizing a two-phase mixed approach as a two-phase flow. In addition, simulations were run in a slow flow state using the finite volume method. The mean Nusselt number and performance evaluation criteria (PEC) were studied for different Darcy and Hartmann numbers. The results show that the amount of heat transfer coefficient increases with increasing the number of Hartmann and Darcy. In addition, the composition of the nanofluid in the base fluid enhanced the PEC in all instances. Furthermore, the PEC has gained its highest value at the conditions relating to the permeable porous medium.

scholarly journals Numerical study of heat transfer in a porous medium of steel balls

2019 ◽  
Vol 23 (1) ◽  
pp. 271-279
Author(s):  
Mehmet Pamuk
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Numerical Study ◽  
Fluid Phase ◽  
Commercial Software ◽  
Number Range ◽  
Unidirectional Flow ◽  
Flow Through ◽  
Steel Balls

In this study, heat transfer in unidirectional flow through a porous medium with the fluid phase being water is analyzed using the commercial software Comsol?. The aim of the study is to validate the suitability of this package for similar problems regarding heat transfer calculations in unidirectional flow through porous media. The porous medium used in the study is comprised of steed balls of 3 mm in diameter filled in a pipe of 51.4 mm inner diameter. The superficial velocity range is 3-10 mm/s which correspond to a Reynolds number range of 150-500 for an empty pipe. Heat is applied peripherally on the outer surface of the pipe at a rate of 7.5 kW/m2 using electrical ribbon heaters. The numerical results obtained using the commercial software Comsol? are compared with those obtained in the experiments once conducted by the author of this article. Results have shown that Comsol? can generate reliable results in heat transfer problems through porous media, provided all parameters are selected correctly, thus making it unnecessary to prepare expensive experimental set-ups and spending extensive time to conduct experiments.

Numerical Prediction of Evaporation Processes in Porous Media Combustors

2007 ◽  
Author(s):  
C. Periasamy ◽  
A. Saboonchi ◽  
S. R. Gollahalli
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Numerical Study ◽  
Mean Value ◽  
Pollutant Emissions ◽  
Fuel Spray ◽  
Vapor Concentration ◽  
Fuel Vapor ◽  
Computational Domain ◽  
The Mean

This paper presents a numerical study of evaporation characteristics of liquid fuel spray in porous media. A two-energy equation model was employed to predict solid and gas phase temperatures. Governing equations were solved on a two-dimensional axisymmetric computational domain of 2.15 × 20 cm. An air-blast atomizer model was used to inject kerosene fuel spray on to the porous medium. Combustion in porous media was simulated by using a uniform volumetric heat source in the porous region. Numerical results were obtained with a commercial code Fluent 6.0. For a heat feedback rate of 1% of average heat input, the porous medium attained a temperature of 465 K. This data agreed well with experimental data obtained by infrared imaging. With an increase in heat feedback rate, the porous medium temperature also increased. Surface temperature distribution in porous media for different heat feedback rates was predicted. Results indicate that the transverse distribution was uniform within 1.5% of the mean value. Droplet diameter was smaller in spray core upstream of porous medium and increased radially due to the swirling action imparted to the atomizing air. Transverse vapor concentration results downstream of porous medium show that the distribution was uniform within 5% of the mean value, which demonstrates that porous medium uniformly distributes the fuel vapor-air mixture. The spatially homogeneous reactant mixture is important to achieve good combustion, reduce pollutant formation, and minimize instabilities in practical combustors. Effects of equivalence ratio and flame temperature on transverse vapor concentration profiles were also numerically studied. Porous media combustors could be used in gas turbine and industrial burner applications to reduce pollutant emissions.

scholarly journals MODELING OF POROUS MEDIA BY THE LATTICE BOLTZMANN METHOD

2020 ◽  
Vol 42 (3) ◽  
pp. 23-28
Author(s):  
A.A. Avramenko ◽  
A.I. Tyrinov ◽  
V.E. Domashev ◽  
A.V. Kovalenko
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Kinetic Equations ◽  
Darcy Law ◽  
Hydrodynamic Drag ◽  
Flows In Porous Media ◽  
Microscopic Models ◽  
Simulated System ◽  
Integral Characteristics ◽  
Boltzmann Method

The principles of modeling heat and mass transfer and hydrodynamics of flows in porous media using the lattices Boltzmann method are considered. The methodology for implementing the Darcy law for the lattices Boltzmann method is shown. In contrast to traditional numerical schemes based on discretization of continuous medium equations, the lattices Boltzmann method is based on microscopic models and mesoscopic kinetic equations. The fundamental idea of the lattices Boltzmann method is to build such simplified kinetic models that include the existing physics of microscopic or mesoscopic processes so that the macroscopic averaged properties correspond to the required macroscopic equations. The main premise of using this simplified method is that the macroscopic dynamics of a fluid is the result of the collective behavior of many microscopic particles of the system. There are two approaches to modeling porous media using the lattices Boltzmann method. The first of them consists in modeling the spatial structure of the simulated system. Therefore, no additional factors need to be considered. The second approach is that the integrated characteristics of the porous medium (Darcy and Forheimer laws) are used to take into account the effect of porosity on the flow. The purpose of this paper is to show the realization of the linear law of hydrodynamic drag (Darcy) in porous media for the lattices Boltzmann method. Usually, the main goal of direct modeling is to determine the integral characteristics of a porous medium. The work considers the flow of fluid through a porous channel, which is formed between two flat walls. A method for implementing the Darcy law in the lattices Boltzmann method is shown. This work will help to simulate the heat transfer and hydrodynamics of flows in porous media without the use of commercial packages.

An Analytical Study for Fluid Flow in Porous Media Imbedded Inside a Channel With Moving or Stationary Walls Subjected to Injection/Suction

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Hamid Reza Seyf ◽  
Seyed Moein Rassoulinejad-Mousavi
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Numerical Study ◽  
Nonlinear Ordinary Differential Equation ◽  
Flow In Porous Media ◽  
Analytical Models ◽  
Vapor Flow ◽  
Brinkman Equations ◽  
Various Boundary Conditions

This paper reports a new analytical solution for 2D Darcy-Brinkman equations in porous channels filled with porous media subjected to various boundary conditions at walls. The governing equations of fluid flow through porous medium are reduced to a nonlinear ordinary differential equation (ODE) based on physics of fluid flow. The obtained ODE is solved analytically using homotopy perturbation method (HPM). The analytical models for velocity profile and pressure distribution along the length of channel are validated with data available in the open literature and an independent numerical study using finite volume method (FVM). It was shown that there is an excellent agreement between the presented models and the results of the CFD and previous works. Finally, the effects of Reynolds (Re) and Darcy (Da), numbers suction or injection parameters (α,β) and wall axial velocity coefficients (λ and γ) on velocity profiles and pressure drop in different cases are investigated. The models are applicable to analyze flow in channels filled with and without porous media for both moving and stationary walls and can be used to predict flow in micro and macro channels and over stretching sheets in porous medium as well as study of vapor flow in evaporator section of flat plate heat pipes.

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