An experimental study on the heat transport in porous media convection

We investigate the heat transport in porous media convection (PMC) over a wide Rayleigh–Darcy number range of 26.8 less than or slanted equals upper R a less than or slanted equals 2.62 times 10 Superscript 5 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mn>26.8</mml:mn> <mml:mo>⩽</mml:mo> <mml:mi>R</mml:mi> <mml:mi>a</mml:mi> <mml:mo>⩽</mml:mo> <mml:mn>2.62</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>5</mml:mn> </mml:msup> </mml:math> $26.8\leqslant Ra\leqslant 2.62\times 10^5$ , and a Darcy number range of 6.18 times 10 Superscript negative 7 Baseline less than or slanted equals upper D a less than or slanted equals 1.21 times 10 Superscript negative 5 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mn>6.18</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:msup> <mml:mo>⩽</mml:mo> <mml:mi>D</mml:mi> <mml:mi>a</mml:mi> <mml:mo>⩽</mml:mo> <mml:mn>1.21</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:math> $6.18\times 10^{-7}\leqslant Da\leqslant 1.21\times 10^{-5}$ . In the experiments, we employ 3D-printed lattice structures as the solid porous matrix and water as the working fluid. Quantitative analyses of the porous medium Nusselt number italic Nu Subscript m <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Nu</mml:mtext> </mml:mrow> <mml:mi>m</mml:mi> </mml:msub> </mml:math> $ \textit{Nu}_m$ and local temperature statistics reveal that the present system undergoes a transition through five distinct regimes: (I) conduction, (II) convection, (III) oscillation, (IV) transition, (V) classical Rayleigh–Bénard convection. This transitional process bridges the gap between Rayleigh–Darcy-like behaviour and Rayleigh–Bénard-like behaviour in PMC. By varying the permeability of the matrix, we further examine the role of the Darcy number italic Da <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Da</mml:mtext> </mml:mrow> </mml:math> $ \textit{Da}$ , which turns out to have a profound impact on the transitional processes across different regimes. Flow field measurements reveal that the flow structures within regime IV and regime V evolve from several horizontally stacked convection rolls to a single-roll structure, and the pore-scale Reynolds numbers both exceed unity in these two regimes. Finally, we report the corresponding phase diagram in the italic Ra <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Ra</mml:mtext> </mml:mrow> </mml:math> $ \textit{Ra}$ – italic Da <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Da</mml:mtext> </mml:mrow> </mml:math> $ \textit{Da}$ space.