Macroscale lattice-Boltzmann methods for low Peclet number solute and heat transport in heterogeneous porous media

2010 ◽  
Vol 46 (7) ◽  
Author(s):  
S. D. C. Walsh ◽  
M. O. Saar
Keyword(s):  
Porous Media ◽  
Heat Transport ◽  
Lattice Boltzmann ◽  
Peclet Number ◽  
Heterogeneous Porous Media ◽  
Lattice Boltzmann Methods ◽  
Péclet Number

Nanofluid Impinging Jets in Porous Media

2016 ◽  
Vol 7 ◽  
pp. 84-113
Author(s):  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Sergio Nardini ◽  
D. Ricci
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Rayleigh Number ◽  
Peclet Number ◽  
Pure Water ◽  
Particle Diameter ◽  
Target Surface ◽  
Impinging Jets ◽  
Local Thermal Equilibrium ◽  
Péclet Number

Heat transfer enhancement technology has the aim to develop more efficient systems as demanded in many applications in the fields of automotive, aerospace, electronics and process industry. A possible solution to obtain efficient cooling systems is represented by the use of confined impinging jets. Moreover, the introduction of nanoparticles in the working fluids can be considered in order to improve the thermal performances of the base fluids. In this paper a numerical investigation on mixed convection in confined slot jets impinging on a porous media by considering pure water or Al2O3/water based nanofluids is described. A two-dimensional model is developed and different Peclet numbers and Rayleigh numbers were considered. The particle volume concentrations ranged from 0% to 4% and the particle diameter is equal to 30 nm. The target surface is heated by a constant temperature value, calculated according to the value of Rayleigh number. The distance of the target surface is five times greater than the slot jet width. A single-phase model approach has been adopted in order to describe the nanofluid behaviour while the hypothesis of non-local thermal equilibrium is considered in order to simulate the behaviour in the porous media which is featured by a porosity value of 0.87. The aim consists into study the thermal and fluid-dynamic behaviour of the system. Results show increasing values of the convective heat transfer coefficients for increasing values of Peclet number and particle concentration. This behaviour is more evident at low Peclet number values and Rayleigh number ones.

Cascaded collision lattice Boltzmann model (CLBM) for simulating fluid and heat transport in porous media

2017 ◽  
Vol 72 (3) ◽  
pp. 211-232 ◽  
Author(s):  
Nimit Shah ◽  
Purbarun Dhar ◽  
Sampath Kumar Chinige ◽  
Martin Geier ◽  
Arvind Pattamatta
Keyword(s):  
Porous Media ◽  
Heat Transport ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Transport In Porous Media ◽  
Boltzmann Model

Solidification With a Throughflow in a Porous Medium

1992 ◽  
Vol 114 (3) ◽  
pp. 675-680
Author(s):  
T. Banerjee ◽  
C. Chang ◽  
W. Wu ◽  
U. Narusawa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Analytical Solutions ◽  
Peclet Number ◽  
Flow In Porous Media ◽  
Circular Pipe ◽  
Parallel Plates ◽  
Péclet Number ◽  
Solid Interface

A steady throughflow in a porous medium is studied in the presence of a solidified layer due to cooling of the walls. Under the assumption of a moderately sloped melt-solid interface, analytical solutions are obtained for both a flow between parallel plates and a circular pipe. Differences and similarities are examined between the Darcian and the Brinkman porous media, as well as the effects of various parameters, such as the Peclet number, the ratio of diffusivities in the longitudinal and the lateral directions, and a parameter indicating the degree of wall cooling and flow heating, on thermofluid structure of a flow in porous media accompanied by solidification.

Effect of Diffusion on Dispersion

SPE Journal ◽  
2010 ◽  
Vol 16 (01) ◽  
pp. 65-77 ◽  
Author(s):  
Raman K. Jha ◽  
Steven L. Bryant ◽  
Larry W. Lake
Keyword(s):  
Porous Media ◽  
Peclet Number ◽  
Plug Flow ◽  
Nonlinear Dependence ◽  
Hydrodynamic Dispersion ◽  
Direction Transverse ◽  
Péclet Number ◽  
Wide Range ◽  
And Diffusion ◽  
Stream Splitting

Summary It is known that dispersion in porous media results from an interaction between convective spreading and diffusion. However, the nature and implications of these interactions are not well understood. Dispersion coefficients obtained from averaged cup-mixing concentration histories have contributions of convective spreading and diffusion lumped together. We decouple the contributions of convective spreading and diffusion in core-scale dispersion and systematically investigate interaction between the two in detail. We explain phenomena giving rise to important experimental observations such as Fickian behavior of core-scale dispersion and power-law dependence of dispersion coefficient on Péclet number. We track movement of a swarm of solute particles through a physically representative network model. A physically representative network model preserves the geometry and topology of the pore space and spatial correlation in flow properties. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes’ equation. Paths of all solute particles are deterministically known in the absence of diffusion. Thus, we can explicitly investigate purely convective spreading by tracking the movement of solute particles on these streamlines. Then, we superimpose diffusion and study dispersion in terms of interaction between convective spreading and diffusion for a wide range of Péclet numbers. This approach invokes no arbitrary parameters, enabling a rigorous validation of the physical origin of core-scale dispersion. In this way, we obtain an unequivocal, quantitative assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion in flow through porous media. Convective spreading has two components: stream splitting and velocity gradient in pore throats in the direction transverse to flow. We show that, if plug flow occurs in the pore throats (accounting only for stream splitting), all solute particles can encounter a wide range of independent velocities because of velocity differences between pore throats and randomness of pore structure. Consequently, plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading (in this case, only stream splitting), and, consequently, dispersion is simply the sum of convective spreading and diffusion. In plug flow, hydrodynamic dispersion varies linearly with the pore-scale Péclet number when diffusion is small in magnitude compared to convective spreading. For a more realistic parabolic velocity profile in pore throats, particles near the solid surface of the medium do not have independent velocities. Now, purely convective spreading (caused by a combination of stream splitting and variation in flow velocity in the transverse direction) is non-Fickian. When diffusion is nonzero, solute particles in the low-velocity region near the solid surface can move into the main flow stream. They subsequently undergo a wide range of independent velocities because of stream splitting, and, consequently, dispersion becomes asymptotically Fickian. In this case, dispersion is a result of an interaction between convection and diffusion. This interaction results in a weak nonlinear dependence of dispersion on Péclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data for a broad range of Péclet numbers. Thus, the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (1) stream splitting of the solute front at every pore, causing independence of particle velocities purely by convection; (2) velocity gradient in pore throats in the direction transverse to flow; and (3) diffusion. Taylor's dispersion in a capillary tube accounts only for the second and third of these phenomena, yielding a quadratic dependence of dispersion on Péclet number. Plug flow in the bonds of a physically representative network accounts only for the first and third phenomena, resulting in a linear dependence of dispersion on Péclet number. When all the three phenomena are accounted for, we can explain effectively the weak nonlinear dependence of dispersion on Péclet number.

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