Modelling the Nu-Ra relationship to establish the intrinsic permeability of coarse open-graded materials from natural air convection tests in a 1 m3 cell

Abstract

Natural air convection can substantially increase heat extraction rate from coarse open-graded granular materials. The initiation and extent of convection is strongly associated with the intrinsic permeability (K) of these materials. This paper presents a numerical study on natural air convection based on large-scale laboratory experiments with a sample size of 1 m3. The model allows modification of the existing analytical Nusselt (Nu) and Rayleigh (Ra) number relationship that was developed for a perfectly insulated and impervious cell with a square cross section. The Nu-Ra relationship derived from the numerical model accounts for the effect of side insulation, the presence of interface layers between the sample and temperature boundaries, and heat flux measurements that do not cover the entire horizontal surface. The model is based on a coupled heat and mass transfer with intra-pore convection, and was modeled using Darcy’s law assuming linear flow conditions. The numerical model shows that the resulting Nu-Ra number relationship is dependent on the effective thermal conductivity (ke) of the sample. The final model is used to derive Nu-Ra number relationships for a ke ranging from 0.1 to 1.0 W/m °C. Heat transfer test results on very coarse open-graded materials are re-analysed with the developed Nu-Ra relationship to assess their intrinsic permeability. The procedure is applied to three crushed rock materials (20/120, 40/120 and 20/250 mm), natural cobbles (90/210 mm), and foam glass material (10/60 mm). The results show a varying degree of overestimation of the original K values based on the analytical Nu-Ra relationship compared to the K values based on the Nu-Ra relationship derived from the numerical model. The re-established K values are 16, 22 and 12% lower for the 20/120, 40/120 and 20/250 mm crushed rock material, respectively, 26% lower for natural cobbles, and 8% lower for foam glass material. Overall, the numerical model shows the importance of a test-setup- and material-specific Nu-Ra relationship for more precise establishment of K values.