Begell House Inc.
Journal of Porous Media
JPM
1091-028X
23
5
2020
H2 FORCED CONVECTION IN GENERAL CROSS-SECTION DUCTS FILLED WITH A POROUS MEDIUM—APPLICATION TO CIRCULAR SEGMENT DUCT (FORCED CONVECTION IN POROUS MEDIUM DUCT)
413-423
10.1615/JPorMedia.2020027292
C. Y.
Wang
Department of Mathematics and Mechanical Engineering, Michigan State University, East
Lansing, Michigan 48824, USA
Darcy-Brinkman
thermal convection
Ritz
circular segment
Variational methods are established for constant-flux forced convection in a duct filled with a porous medium. The efficient method can be applied to ducts of general cross section with H1 or H2 heat transfer. The method is then applied to the porous circular segment duct. In particular, the uneven heat flux H2 heat transfer is studied for the first time.
CONDITIONS OF EVOLUTION IN TIME OF CONCENTRATION BOUNDARY LAYERS IN TWO-MEMBRANE SYSTEM
425-444
10.1615/JPorMedia.2020030939
Slawomir
Grzegorczyn
Department of Biophysics, School of Medicine with the Division of Dentistry in Zabrze,
Medical University of Silesia, 19 H. Jordan Str., 41808 Zabrze, Poland
Andrzej
Slezak
Institute of Health and Nutrition Sciences, Department of Biophysics, Czestochowa University
of Technology, 36B Armia Krajowa Al, 42200 Czestochowa, Poland
concentration polarization
bacterial cellulose
diffusion
gravitational convection
hydrodynamic instabilities
Kedem-Katchalsky equations
membrane transport
The conditions of appearance of hydrodynamic instabilities at membrane surfaces in a two-membrane system with membranes located in horizontal planes and with solution with a higher concentration and higher density in a chamber between membranes were studied. The method of measurement of voltage between Ag|AgCl electrodes immersed directly into solutions in outside chambers, symmetrically to membranes, was used. Two types of membranes−bacterial cellulose membrane and polymer membrane−were investigated. The results from the measurements show that the time of appearance of hydrodynamic instabilities in the two-membrane system depends on the initial KCl concentrations in chambers. An increase of quotient of concentrations on the membranes at an initial moment causes a nonlinear increase of time of appearance of hydrodynamic instabilities. Besides, the average frequency of voltage pulsations caused by hydrodynamic instabilities in the two-membrane system in a selected range of time also increases nonlinearly with the increase of quotient of concentrations at the initial moment for different membranes as well as for the same membranes. Analysis of time characteristics of voltage in the two-membrane system allows identifying two ranges of voltage change: a smooth decrease in time for diffusional reconstruction of concentration polarization of membranes and pulsating character of voltage changes in time for conditions with diffusion and hydrodynamic instabilities in near membrane area. Besides, the mathematical model elaborated for the two-membrane system shows that for different membranes the distribution of concentration in chambers is asymmetric, while for the same membranes the distribution of concentration is symmetrical with respect to membranes.
HEAT TRANSFER CHARACTERISTICS OF A SINGLE FRACTURE WITH DIFFERENT FRACTURE SURFACE ROUGHNESS LEVELS AND APERTURE VARIATIONS
445-463
10.1615/JPorMedia.2020027283
Kelvin
Bongole
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, China
Jun
Yao
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, China
Ying
Xin
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, China
Zhuang
Li
Korea Institute of Civil Engineering and Building Technology, Goyang 10223, Korea
Asif
Mehmood
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, China
Kai
Zhang
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, China
Chuanyin
Jiang
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, China
Zhixue
Sun
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao
266580, China
fracture roughness
aperture variation
EGS
porous media
heat transfer
THM
Understanding the flow pattern along a fracture plane is essential to achieving efficient heat extraction in enhanced geothermal systems (EGSs). The nature of surface roughness and aperture variation in fractures influences the heat extraction and performance of geothermal reservoirs due to flow disparity. In this study, aperture pattern and fracture surface roughness are derived from statistical distribution parameters to investigate the heat transfer characteristics of a single fracture. A geometric variation of thermal and mechanical (TM) parameters of the rock matrix is randomly distributed in three-dimensional space, and a fully-coupled thermo-hydro-mechanical (THM) model is presented. The result shows that rough fracture surfaces with small constant aperture, and varying apertures with higher standard deviation in their distribution, exhibit slower production temperature decline and improved heat and power generation during the extraction period as reduced fracture flow occurs within them. For the same aperture pattern, higher roughness levels of the fracture surface have improved power output and less decline in production temperature than smooth fracture. A small production temperature decline and improved power generation was observed considering a varying TM parameter model. Large values of constant and varying apertures exhibit high stress across the fracture and on the matrix block, evident by the fracture permeability evolution and matrix stress distribution.
NON-NEWTONIAN FLOW IN DEFORMABLE POROUS MEDIA: MODELING AND SIMULATIONS OF COMPRESSION MOLDING PROCESSES
465-476
10.1615/JPorMedia.2020027274
Umair
Farooq
Department of Mathematics, Capital University of Science and Technology, Islamabad 44000,
Pakistan
J. I.
Siddique
Department of Mathematics, Penn State University- York Campus, York, Pennsylvania
17403-3326, USA
power law fluid
compression molding
deformable porous media
mixture theory
solid volume fraction
The aim of this study is to develop a mathematical model based on power law fluid using mixture theory. The resulting system is solved numerically and graphs are produced to highlight the unidirectional compression molding process. In this industrial process, a piston operates on the top of the pile to compress the preimpregnated layers. The moving domain problem is modeled using Eulerian coordinates, and then transformed to fixed domain using Lagrangian coordinates. The dynamics are controlled by velocity of piston or pressure applied on the piston. We find that there is a homogeneous increase in solid volume fraction for shear thickening fluid as compared to shear thinning fluid.
ELECTRO-OSMOTIC FLOW IN A MICROCHANNEL CONTAINING A POROUS MEDIUM WITH COMPLEX WAVY WALLS
477-495
10.1615/JPorMedia.2020026114
Dharmendra
Tripathi
Department of Mathematics, National Institute of Technology, Uttarakhand -246174, India
Shashi
Bhushan
Department of Mechanical Engineering, Manipal University, Jaipur-303007, India
Osman Anwar
Beg
Gort Engovation-Aerospace, Medical and Energy Engineering, Gabriel's Wing House, 15
Southmere Avenue, Bradford, BD73NU, United Kingdom; Fluid Mechanics, Department of Mechanical and Aeronautical Engineering, Salford
University, M54WT, England, United Kingdom
axial electric force
Debye length
permeability
Helmholtz-Smoluchowski velocity
porous medium
trapping
In the present paper, we simulate the electro-kinetic transport of aqueous solution through a microchannel containing porous media. The microchannel walls are simulated as a complex wavy surface and are modeled by superimposing the three wave functions of different amplitudes but the same wavelength. The microchannel contains an isotropic, homogeneous porous medium, which is analyzed with a generalized Darcy law. The nonlinear-coupled governing equations for mass, momentum, and electrical potential conservation are simplified using low Reynolds number and long wavelength approximations, and Debye electrokinetic linearization. Following nondimensional transformation of the linearized boundary value problem, closed-form analytical solutions are presented for the velocity components, pressure gradient, local wall shear stress, average flow rate, and stream function subject to physically appropriate boundary conditions. Validation with a finite difference method is also conducted. The effects of permeability parameter, Debye length (i.e., characteristic thickness of electrical double layer), and electro-osmotic velocity on flow characteristics are illustrated graphically and interpreted at length. The study finds applications in chromatography, hybrid electro-osmotic micropumps, transport phenomena in chemical engineering, and energy systems exploiting electrokinetics.
THERMAL DIFFUSIVITY VARIATION EFFECT ON A HYDRO-THERMAL CONVECTIVE FLOW IN A POROUS MEDIUM
497-515
10.1615/JPorMedia.2020028604
Dambaru
Bhatta
School of Mathematical and Statistical Science, University of Texas Rio Grande Valley,
Edinburg, Texas 78539, USA
Daniel N.
Riahi
School of Mathematical and Statistical Science, University of Texas Rio Grande Valley,
Edinburg, Texas 78539, USA
diffusivity
convective
porous media
weakly nonlinear
Rayleigh number
We consider a hydrothermal convective flow in a porous medium to investigate the effect of the vertical rate of change in thermal diffusivity. Using a weakly nonlinear approach, we derive the linear and first-order systems assuming a no-flow basic state system. The solutions for the linear and first-order systems are computed numerically using both the fourth-order Runge-Kutta and shooting methods. Numerical results obtained in this study show a stabilizing effect on the dependent variables for the case of a positive vertical rate of change in diffusivity, whereas a destabilizing effect is noticed for the case of a negative vertical rate of change in diffusivity. The present results indicate that convective flow driven by the buoyancy force is more effective if thermal diffusivity is weaker, while the opposite result holds for a stronger diffusivity effect. In particular, both velocity and convective temperature decrease with increasing diffusivity, while they increase with decreasing diffusivity. At the middle of the layer (z = 0) for x = 0, the contribution of the linear and first-order solutions to the velocity component are 0.3345, 0.3031, and 0.3679 for the respective values 0.0, 0.6, and -0.4 of the diffusivity parameter. For temperature, these contributions are 0.0167, 0.0116, and 0.0229, respectively. Some other quantitative results are provided in tabular form.