We report pore-scale statistical properties of temperature and thermal energy
dissipation rate in a two-dimensional porous Rayleigh-B\'enard (RB) cell.
High-resolution direct numerical simulations were carried out for the fixed
Rayleigh number (Ra) of 109 and the Prandtl numbers (Pr) of 5.3 and
0.7. We consider sparse porous media where the solid porous matrix is
impermeable to both fluid and heat flux. The porosity (Ο) range 0.86β€Οβ€0.98, the corresponding Darcy number (Da) range
10β4<Da<10β2 and the porous Rayleigh number (Raβ=Raβ Da) range
105<Raβ<107. Our results indicate that the plume dynamics in
porous RB convection are less coherent when the solid porous matrix is
impermeable to heat flux, as compared to the case where it is permeable. The
averaged vertical temperature profiles remain almost a constant value in the
bulk, whilst the mean square fluctuations of temperature increases with
decreasing porosity. Furthermore, the absolute values of skewness and flatness
of the temperature are much smaller in the porous RB cell than in the canonical
RB cell. We found that intense thermal energy dissipation occurs near the top
and bottom walls, as well as in the bulk region of the porous RB cell. In
comparison with the canonical RB cell, the small-scale thermal energy
dissipation field is more intermittent in the porous cell, although both cells
exhibit a non-log-normal distribution of thermal energy dissipation rate. This
work highlights the impact of impermeable solid porous matrices on the
statistical properties of temperature and thermal energy dissipation rate, and
the findings may have practical applications in geophysics, energy and
environmental engineering, as well as other fields that involve the transport
of heat through porous media.Comment: 30 pages, 16 figure