Session: 16-01-01: NSF-funded Research (Grad & Undergrad)
Paper Number: 77208
Start Time: Wednesday, 02:25 PM
77208 - Comparison of Porescale and Volume-Averaged Simulations of Thermal Convection in Porous Media
The study of thermal convection in porous media is of both fundamental and practical interest. Some examples in nature and industry include heat transfer in volcanic rock systems, subseafloor thermohaline convection, sequestration of carbon dioxide, hydrothermal convection for extraction of geothermal energy, forced convection through high-porosity metal foams, and thermochemical reactions in reticulated porous ceramic structures. Conventionally, numerical studies in this field have relied on volume-averaged formulations based on the Darcy–Oberbeck–Boussinesq (DOB) equations. In the DOB equations, the dimensionless Rayleigh number (Ra) controls the “strength” of convection, where pore scale effects enter through only the porosity. The Rayleigh number describes the ratio of buoyancy to viscosity multiplied by the Darcy number (Da), where Da characterizes the ratio between permeability and a characteristic cross-sectional area. Typically, the effect of Ra is compared by evaluating the dimensionless Nusselt number (Nu), which describes the efficiency of heat transfer, defined as the ratio of the total heat transfer rate (conduction and convection) to the conductive heat transfer rate at a wall surface.
Numerous experiments and theoretical/computational studies have been devoted to obtaining quantitative relationships between Ra and Nu. Following investigations in Rayleigh-Bernard convection (thermal convection in the absence of porous media), these relations are typically suggested in the form of Nu=aRab where a is a constant and b is a scaling exponent. Experiments thus far have demonstrated largely non-linear and scattered Nu-Ra behavior, i.e. a and b are not constant. For Ra > 1000, some authors have suggested scaling exponents as low as 0.319. However, in comparison, numerical models based on the DOB equations have predicted linear Nu-Ra relationships with scaling exponents in the range of 0.8-0.95. This discrepancy raises questions on the range of applicability of the DOB equations and the assumptions used in their derivation, namely the neglection of momentum dispersion, thermal dispersion, and viscous diffusion.
Recent studies in the field of density-driven mass convection in porous media have suggested that “pore-scale parameters” not captured by the DOB equations may have significant effects on convection dynamics. While this gives some insights into the observed Nu-Ra discrepancy, mass transfer typically considers the solid phase impermeable, while for heat transfer, both fluid and solid phases will participate in the transport process, and the interface conjugate conditions are evident between the phases. Thus, in order to accurately simulate the thermal convection in porous media and also to gain more insights into the accuracy of the DOB equations, we perform pore-scale direct numerical simulations (DNS) of a simplified two-dimensional porous domain and compare to results obtained from the DOB equations for thermal convection.
From our studies, we find that both the pore size and conjugate heat transfer have substantial effects on the Nusselt number and thermal plume structures. We show that the frequency of plume columns increases as the solid-to-fluid thermal conductivity ratio, ks/kf, decreases and that interior plumes become larger as pore size increases. In comparing different porosities, we find that both DNS and DOB results predict an increase in Nu with porosity for the cases with ks/kf < 1, and the opposite is noticed for ks/kf > 1. In considering the conjugate heat transfer effect, we show that the magnitude of the Nusselt number decreases significantly as ks/kf increases. At Ra < 2000, both DOB and DNS results predict scaling exponents between 0.8-0.95, however, for high Ra values, the DNS results show divergence from this scaling and tend towards smaller values, which is consistent with experimental results. Thus, we conclude that the scaling of the Nusselt number is affected by not only porosity, but also by pore-size and conjugate heat transfer, which can only be fully captured in the pore-scale DNS.
Presenting Author: David Korba Mississippi State University
Authors:
David Korba Mississippi State UniversityLike Li Mississippi State University
Comparison of Porescale and Volume-Averaged Simulations of Thermal Convection in Porous Media
Paper Type
NSF Poster Presentation