Abstract
The vertical throughflow effect on the onset of penetrative convection in a horizontal air sublayer overlying a porous sublayer is investigated in the gravitational field. The porous sublayer contains an internal heat source with the volumetric strength linearly dependent on the solid fraction. It has been found that the depth ratio and solid fraction are destabilizing at any direction and velocity of the throughflow. The upward and downward throughflows can be both stabilizing and destabilizing in the range of the Peclet number of \(\mathrm{{ - }}6<\mathrm{{Pe}}<6\) considered. The study has revealed that the non-monotonic dependence of the onset internal Darcy-Rayleigh number versus the Peclet number may get a second minimum in addition to the first dominant one. It is due to an abrupt change in the critical wave number of convection patterns. A special attention is paid to the local and large-scale convective regimes which replace each other with the variation of the Peclet number, solid fraction and depth ratio. One has obtained a regime map which includes a demarcation line between the two regimes and a region of parameters for the bimodal marginal stability curves.
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Abbreviations
- b :
-
ratio of volumetric heat capacities
- C :
-
specific heat capacity
- d :
-
depth ratio
- \(\mathrm{{Da}}\) :
-
Darcy number
- \(\mathbf{{g}}\) :
-
acceleration of gravity, \(- g\mathbf{{\gamma }}\)
- \({h_a}\) :
-
thickness of air sublayer
- \({h_p}\) :
-
thickness of porous sublayer
- K :
-
permeability
- k :
-
wave number
- P :
-
pressure excluding the hydrostatic additive
- \(\mathrm{{Pe}}\) :
-
Peclet number
- \({\Pr _p}\) :
-
Prandtl number in the porous sublayer
- \({Q_s}\) :
-
volumetric heat source strength in the solid phase
- \({\mathrm{{R}}_I}\) :
-
internal Darcy-Rayleigh number normalized by the solid fraction
- \(\mathrm{{R}}{\mathrm{{a}}_I}\) :
-
internal Darcy-Rayleigh number, \(\phi {\mathrm{{R}}_I}\)
- T :
-
temperature
- t :
-
time
- \(\mathbf{{U}}\) :
-
velocity of throughflow, \(\mathbf{{U}} = U\mathbf{{\gamma }}\)
- \({\mathbf{{V}}_a}\) :
-
velocity in the air sublayer
- \({\mathbf{{V}}_p}\) :
-
seepage velocity in the porous sublayer
- x :
-
coordinate of the longitudinal axis
- z :
-
coordinate of the transversal axis
- \(\beta\) :
-
thermal expansion coefficient
- \(\mathbf{{\gamma }}\) :
-
unit vector of the z-axis
- \(\kappa\) :
-
ratio of thermal conductivities, \({\kappa _p}/{\kappa _a}\)
- \({\kappa _a}\) :
-
thermal conductivity of the air sublayer
- \({\kappa _p}\) :
-
thermal conductivity of the porous sublayer
- \(\lambda\) :
-
growth rate of disturbances
- \(\nu\) :
-
kinematic viscosity of air
- \({\rho _0}\) :
-
air density at \(T = {T_0}\)
- \({\chi _{eff}}\) :
-
effective thermal diffusivity of the porous sublayer, \({\kappa _p}/{\left( {\rho _0}C\right) }_a\)
- \({\chi _a}\) :
-
thermal diffusivity of the air sublayer, \({\kappa _a}/{\left( {\rho _0}C\right) }_a\)
- \(\phi\) :
-
solid fraction
- \(\nabla\) :
-
nabla operator
- \(\Theta\) :
-
dimensionless temperature deviation from a reference value of \({T_0}\)
- l :
-
the lower boundary of the porous sublayer
- a :
-
air sublayer
- p :
-
porous sublayer
- s :
-
solid
- u :
-
the upper boundary of the air sublayer
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The work was supported by the Russian Science Foundation (Grant No. 21-71-10045), https://rscf.ru/en/project/21-71-10045/.
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Ekaterina Kolchanova: Conceptualization, Methodology, Investigation, Writing- Reviewing and Editing, Funding acquisition. Rafil Sagitov: Software, Validation, Investigation, Writing- Original draft preparation.
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Kolchanova, E., Sagitov, R. Throughflow Effect on Local and Large-scale Penetrative Convection in Superposed Air-porous Layer with Internal Heat Source Depending on Solid Fraction. Microgravity Sci. Technol. 34, 52 (2022). https://doi.org/10.1007/s12217-022-09971-2
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DOI: https://doi.org/10.1007/s12217-022-09971-2