scholarly journals MACROSCOPIC TURBULENCE MODEL ADJUSTMENT FOR A POROUS MEDIUM MODELED AS AN INFINITE ARRAY OF TRANSVERSALLY-DISPLACED ELLIPTIC RODS

2003 ◽  
Vol 2 (2) ◽  
Author(s):  
M. H. J. Pedras ◽  
M. J. S. De Lemos
Keyword(s):  
Volume Averaging ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Governing Equations ◽  
Periodic Cell ◽  
Aspect Ratios ◽  
Infinite Array ◽  
Model Adjustment ◽  
High Reynolds ◽  
Adjusted Model

Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, , a macroscopic model was proposed for flow in porous media (Pedras and de Lemos, IJHMT 44 (6) 2001). As an outcome of the volume averaging process, additional terms appeared in the equations for k and . These terms were here adjusted assuming the porous structure to be modeled as an infinity array of transversal elliptic rods. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low and high Reynolds formulation, in the periodic cell composing the infinite medium. Different porosity and aspect ratios were investigated. The adjusted model was compared against others types of rods found in the literature, showing similar results.

scholarly journals MACROSCOPIC TURBULENCE MODEL ADJUSTMENT FOR A POROUS MEDIUM MODELED AS AN INFINITE ARRAY OF TRANSVERSALLY-DISPLACED ELLIPTIC RODS

2003 ◽  
Vol 2 (2) ◽  
pp. 73
Author(s):  
M. H. J. Pedras ◽  
M. J. S. De Lemos
Keyword(s):  
Dissipation Rate ◽  
Infinite Medium ◽  
Macroscopic Model ◽  
Governing Equations ◽  
Periodic Cell ◽  
Aspect Ratios ◽  
Infinite Array ◽  
Model Adjustment ◽  
High Reynolds ◽  
Adjusted Model

Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, , a macroscopic model was proposed for flow in porous media (Pedras and de Lemos, IJHMT 44 (6) 2001). As an outcome of the volume averaging process, additional terms appeared in the equations for k and . These terms were here adjusted assuming the porous structure to be modeled as an infinity array of transversal elliptic rods. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low and high Reynolds formulation, in the periodic cell composing the infinite medium. Different porosity and aspect ratios were investigated. The adjusted model was compared against others types of rods found in the literature, showing similar results.

On the Mathematical Description and Simulation of Turbulent Flow in a Porous Medium Formed by an Array of Elliptic Rods

2001 ◽  
Vol 123 (4) ◽  
pp. 941-947 ◽  
Author(s):  
Marcos H. J. Pedras ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Turbulent Flow ◽  
Porous Structure ◽  
Volume Averaging ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Turbulence Structure ◽  
Turbulent Regime ◽  
Periodic Cell ◽  
Initial Work ◽  
Adjusted Model

Many engineering and environmental system analyses can benefit from appropriate modeling of turbulent flow in porous media. Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, ε, a macroscopic model was proposed for such media (IJHMT, 44(6), 1081-1093, 2001). In that initial work, the medium was simulated as an infinite array of cylindrical rods. As an outcome of the volume averaging process, additional terms appeared in the equations for k and ε. These terms were here adjusted assuming now the porous structure to be modeled as an array of elliptic rods instead. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low Reynolds formulation, in the periodic cell composing the medium. Different porosity and Reynolds numbers were investigated. The fine turbulence structure of the flow was computed and integral parameters were presented. The adjusted model constant was compared to similar results for square and cylindrical rods. It is expected that the contribution herein provide some insight to modelers devoted to the analysis of engineering and a environmental systems characterized by a porous structure saturated by a fluid flowing in turbulent regime.

scholarly journals Direct Numerical Simulation of Pore-Scale Trapping Events During Capillary-Dominated Two-Phase Flow in Porous Media

2021 ◽  
Author(s):  
Mosayeb Shams ◽  
Kamaljit Singh ◽  
Branko Bijeljic ◽  
Martin J. Blunt
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Direct Numerical Simulation ◽  
Complex Geometry ◽  
Flow In Porous Media ◽  
Pore Scale ◽  
Contact Lines ◽  
Two Phase ◽  
X Ray ◽  
Aspect Ratios

AbstractThis study focuses on direct numerical simulation of imbibition, displacement of the non-wetting phase by the wetting phase, through water-wet carbonate rocks. We simulate multiphase flow in a limestone and compare our results with high-resolution synchrotron X-ray images of displacement previously published in the literature by Singh et al. (Sci Rep 7:5192, 2017). We use the results to interpret the observed displacement events that cannot be described using conventional metrics such as pore-to-throat aspect ratio. We show that the complex geometry of porous media can dictate a curvature balance that prevents snap-off from happening in spite of favourable large aspect ratios. We also show that pinned fluid-fluid-solid contact lines can lead to snap-off of small ganglia on pore walls; we propose that this pinning is caused by sub-resolution roughness on scales of less than a micron. Our numerical results show that even in water-wet porous media, we need to allow pinned contacts in place to reproduce experimental results.

Row Removal Heat Transfer Study for Pin Fin Arrays

2014 ◽  
Author(s):  
Kathryn L. Kirsch ◽  
Jason K. Ostanek ◽  
Karen A. Thole ◽  
Eleanor Kaufman
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Pin Fin ◽  
Heat Transfer Augmentation ◽  
Aspect Ratios ◽  
Pin Fins ◽  
High Reynolds ◽  
Pin Fin Arrays ◽  
Transfer Study

Arrays of variably-spaced pin fins are used as a conventional means to conduct and convect heat from internal turbine surfaces. The most common pin shape for this purpose is a circular cylinder. Literature has shown that beyond the first few rows of pin fins, the heat transfer augmentation in the array levels off and slightly decreases. This paper provides experimental results from two studies seeking to understand the effects of gaps in pin spacing (row removals) and alternative pin geometries placed in these gaps. The alternative pin geometries included large cylindrical pins and oblong pins with different aspect ratios. Results from the row removal study at high Reynolds number showed that when rows four through eight were removed, the flow returned to a fully-developed channel flow in the gap between pin rows. When larger alternative geometries replaced the fourth row, heat transfer increased further downstream into the array.

scholarly journals Triglobal infinite-wing shock-buffet study

2021 ◽  
Vol 925 ◽  
Author(s):  
Wei He ◽  
Sebastian Timme
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Base Flow ◽  
Sweep Angle ◽  
Aspect Ratios ◽  
Spatially Periodic ◽  
Time Marching ◽  
High Reynolds ◽  
Limiting Case ◽  
Base Flows

This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.

Correlated Compressible and Incompressible Channel Flows

1997 ◽  
Vol 119 (4) ◽  
pp. 911-915 ◽  
Author(s):  
C. Crnojevic´ ◽  
V. D. Djordjevic´
Keyword(s):  
Cross Section ◽  
High Reynolds Number ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Isothermal Flow ◽  
Governing Equations ◽  
Adiabatic Flow ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Reynolds Number Flows

Compressible flow in channels of slowly varying cross section at moderately high Reynolds numbers is treated in the paper by employing some Stewartson-type transformations that convert the problem into an incompressible one. Both adiabatic flow and isothermal flow are considered, and a Poiseuille-type incompressible solution is mapped onto compressible plane in order to generate some exact solutions of the compressible governing equations. The results show striking effects that viscosity may have upon the flow characteristics in this case, in comparison with more conventional high Reynolds number flows.

scholarly journals The Influence of Bioreactor Geometry and the Mechanical Environment on Engineered Tissues

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
J. M. Osborne ◽  
R. D. O’Dea ◽  
J. P. Whiteley ◽  
H. M. Byrne ◽  
S. L. Waters
Keyword(s):  
Shear Stress ◽  
Culture Medium ◽  
Porous Scaffold ◽  
Two Dimensional ◽  
Governing Equations ◽  
Long Wavelength ◽  
Wavelength Limit ◽  
Aspect Ratios ◽  
Three Phase ◽  
Tissue Construct

A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium, and porous scaffold are treated as distinct phases. The bioreactor system is represented by a two-dimensional channel containing a cell-seeded rigid porous scaffold (tissue construct), which is perfused with a culture medium. Through the prescription of appropriate functional forms for cell proliferation and extracellular matrix deposition rates, the model is used to compare the influence of cell density-, pressure-, and culture medium shear stress-regulated growth on the composition of the engineered tissue. The governing equations are derived in O’Dea et al. “A Three Phase Model for Tissue Construct Growth in a Perfusion Bioreactor,” Math. Med. Biol., in which the long-wavelength limit was exploited to aid analysis; here, finite element methods are used to construct two-dimensional solutions to the governing equations and to investigate thoroughly their behavior. Comparison of the total tissue yield and averaged pressures, velocities, and shear stress demonstrates that quantitative agreement between the two-dimensional and long-wavelength approximation solutions is obtained for channel aspect ratios of order 10−2 and that much of the qualitative behavior of the model is captured in the long-wavelength limit, even for relatively large channel aspect ratios. However, we demonstrate that in order to capture accurately the effect of mechanotransduction mechanisms on tissue construct growth, spatial effects in at least two dimensions must be included due to the inherent spatial variation of mechanical stimuli relevant to perfusion bioreactors, most notably, fluid shear stress, a feature not captured in the long-wavelength limit.

Computational Analysis of Fiber Dynamics in Human Nasal Cavity

2020 ◽  
Author(s):  
Jiawei Ma ◽  
Jiyuan Tu ◽  
Lin Tian ◽  
Goodarz Ahmadi
Keyword(s):  
Nasal Cavity ◽  
Transport Processes ◽  
Upper Respiratory Tract ◽  
Governing Equations ◽  
Aspect Ratios ◽  
Model Predictions ◽  
Fiber Dynamics ◽  
Upper Respiratory ◽  
Rotational Motions ◽  
Insight Into

Abstract Elongated particles, such as asbestos and mineral fibers, are considered severe inhalation hazards due to their ability to penetrate into the deep lung. Frequently the dynamic behavior of the fibrous particles is attributed to their unique needle-like geometry. Therefore, understanding the interactions of the inhaled elongated particles with the airflow environment is of great significance. In this study, the transport and deposition of elongated micro-fibers in a realistic human nasal cavity is investigated numerically. The motion of the micro-fiber is resolved by solving the system of equations governing its coupled translational and rotational motions. The governing equations included the drag, the hydrodynamic torques that were evaluated using the Jeffrey model. The influence of the shear lift force was also included in these simulations. The no-slip wall boundary condition for airflow in the airways was used. Since the surface of airways is covered with mucus, when a fiber touches the surface, it was assumed to be deposited with no rebound. The study allows a close look at the non-spherical particle-flow dynamics with respect to the translation, rotation, coupling, and how the rotation affects the particle’s macroscopic transport and deposition properties. A series of simulations for different microfiber diameters and aspect ratios were performed. The simulation results are compared with the existing experimental data, and earlier computational model predictions and good agreements were obtained. The present study also seeks to provide additional insight into the transport processes of microfibers in the upper respiratory tract.

Phase-Field Models of Gravity-Driven Unsaturated Flow in Porous Media

2008 ◽  
Author(s):  
Luis Cueto-Felgueroso ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Preferential Flow ◽  
Unsaturated Flow ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Wetting Front ◽  
Forming Mechanism ◽  
Gravity Driven ◽  
Pattern Forming ◽  
Models Of Gravity

Existing continuum models of multiphase flow in porous media are unable to explain why preferential flow (fingering) occurs during infiltration into homogeneous, dry soil. We identify a relevant pattern-forming mechanism in the dynamics of the wetting front, and present a macroscopic model that reproduces the experimentally observed features of fingered flows. The proposed model reveals a scaling between local and nonlocal interface phenomena in imbibition, and does not introduce new independent parameters. The predictions based on this model are consistent with experiments and theories of scaling in porous media.

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