Direct Numerical Simulation Reveals Heat-Transfer Scaling in Ultimate Regime of Rayleigh-Darcy Convection
Researchers performed direct numerical simulations (DNS) of Rayleigh-Darcy convection in a 3D porous domain across a wide range of Rayleigh numbers, identifying a distinct transition to an 'ultimate regime' at approximately Ra ≈ 4×10⁵. Below this threshold, heat transfer scaling differed from prior high-Ra studies, while above it results closely matched earlier theoretical predictions for the ultimate regime. The findings clarify how porous-media convection behaves at extreme conditions, with implications for geophysical and industrial heat-transfer modeling.
A new preprint posted to arXiv presents direct numerical simulations of Rayleigh-Darcy convection in a three-dimensional porous medium, spanning Rayleigh numbers from 10³ to 10⁶—a range that probes the previously unexplored ultimate convective regime. The Nusselt number (Nu), a measure of heat transfer efficiency, shows an approximately linear dependence on the Rayleigh number (Ra) throughout, but a clear change in slope emerges near Ra ≈ 4×10⁵, marking the onset of the ultimate regime. At lower Ra, the scaling is about 6.25% below values reported in a widely cited 2014 study, while at higher Ra the results fall within 1.24% of an extrapolated ultimate-regime prediction from 2021. Thermally, the simulations reveal that small near-wall structures called protoplumes form and merge into larger columnar megaplumes; as Ra increases, protoplumes become more numerous and finer, enhancing heat transport from walls to the bulk fluid. The thermal boundary-layer thickness scales as Ra⁻¹ and Nu⁻¹, consistent with linear heat-transfer scaling, and thermal dissipation progressively shifts from the boundary layer into the bulk at higher Ra, confirming the efficiency of fine-scale convective structures in the ultimate regime.
What's missing
As a preprint, this work has not yet undergone formal peer review. The study is limited to a specific domain geometry and idealized porous-medium assumptions; how well these DNS results translate to real heterogeneous geological or engineered porous media remains an open question. Computational cost constraints mean the upper Ra boundary (10⁶) may still fall short of asymptotic ultimate-regime behavior.
What different sources said
- arXiv physicsCenter
Ultimate regime in Rayleigh-Darcy Convection
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