Modeling flow in disordered packed beds from pore-scale fluid mechanics

  • Valvatne P
  • Piri M
  • Lopez X
 et al. 
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Abstract

Heat flow through superfluid helium (He II) contained in porous media is examined. In particular, heat transfer experiments were performed on He II contained in a bed of polyethylene spheres of uniform size arranged in random packs. Measured results include the steady state temperature drops across the three random packs of spheres (35, 49, and 98μm diameter) and the associated steady heat inputs. Bath temperatures range from 1.7 to 2.1K to help grasp the superfluid effects. Two pure flow regimes (laminar and turbulent) are decipherable from the heat flux dependence of the temperature gradient. Turbulent results are fitted to an empirically derived turbulent He II heat equation for large channels with an added tortuosity (extra length traveled) term that accounts for the porous media. An average tortuosity of 1.33 was obtained, which is comparable with values of 1.36–1.41 concluded from published work on classical fluid pressure drop across random packed spheres. Laminar permeability and shape factor results are compared to past studies of He II in porous media and in channel flows. The onset of turbulence is determined through a critical heat flux from which a critical Reynolds number is formulated but, does not describe He II turbulence in the normal fluid component. The addition of the laminar and turbulent heat flow equations into a unifying prediction fits the transition regime data within 25%.

Author-supplied keywords

  • 1835 Hydrogeophysics
  • 1847 Modeling
  • 1861 Sedimentation
  • Anisotropic media
  • Chemical Engineering
  • Chemistry
  • Computational fluid dynamics
  • Computed tomography
  • Connectivity
  • Contact points
  • Coordination number
  • Copper foam
  • Correlation
  • Critical value
  • Darcy law
  • Darcy's law
  • Darcy-Forchheimer law
  • Data structures
  • Database systems
  • Elasticity
  • Electrical insulation
  • Engineering
  • Experimental data
  • Finite element
  • Finite volumes
  • Fixed bed
  • Flow
  • Flow through sphere packs
  • Fluid flow modeling
  • Fluid mechanics
  • Forced convection
  • Forchheimer Number
  • Fracture
  • Granular material
  • Heat transfer
  • Heat transfer enhancement
  • Heterogeneous materials
  • Homogenization
  • Hydraulic conductivity
  • Hydraulic fracturing
  • Image processing
  • Imaging
  • Integral range
  • LB
  • Lattice Boltzmann
  • Lattice-Boltzmann
  • Local void ratio
  • Mesoscale bounds
  • Metal foam
  • Metal foams
  • Microscale
  • Microstructure
  • Mixed convection
  • Model validation
  • Modeling
  • Network modelling
  • Non-Darcy behavior
  • Non-Darcy flow
  • Non-Newtonian
  • Non-Newtonian flow
  • Numerical calculation
  • Open-cell aluminum foam
  • Packed bed
  • Packed spheres
  • Parallel computing
  • Particle alignment
  • Particle size distribution
  • Permeability
  • Polymer electrolyte fuel cell
  • Pore network structure
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  • Porous materials
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  • Pressure drop
  • Random composites
  • Random media
  • Rectangular channel flow
  • Relative permeability
  • Representative elementary volume (REV)
  • Representative volume element
  • Representative volume element (RVE)
  • Reservoir simulator
  • Resolution
  • Reynolds number
  • Science
  • Shear-thinning
  • Shear-thinning fluid
  • Simulation
  • Simulators
  • Skeletonization
  • Softening materials
  • Solid fluid coupling
  • Spatial correlation
  • Spheres
  • Stokes flow
  • Superfluid
  • Synchrotron X-ray tomography
  • Texas
  • Transport
  • Turbulent flow
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  • Voronö mosaic
  • Wall effects
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  • anisotropy
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  • conductivity
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  • dams
  • darcy
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  • fractures
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  • heat transfer
  • hydraulic
  • laminar flow
  • low
  • multiphase flow
  • network model
  • neural nets
  • numerical modelling
  • ow through porous media
  • packed beds
  • percolation
  • permeability
  • pore-scale
  • pore-scale modeling
  • porous media
  • porous medium
  • properties
  • relative permeability
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  • rocks
  • s law
  • sandstone
  • sediment transport
  • smoothed particle hydrodynamics
  • sphere pack
  • spheres
  • structural engineering computing
  • tessellation
  • wells

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Authors

  • Per H. Valvatne

  • Mohammad Piri

  • Xavier Lopez

  • Martin J. Blunt

  • R B Bird

  • W E Stewart

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