Adequacy of effective diameter in predicting pressure gradients of air flow through packed beds with particle size distribution

In the late phases of severe accidents in nuclear power plants, in order to ensure the long-term coolability of the debris bed on a reactor containment floor, it is crucial to cool down and stabilize molten core debris, which has an internal heat generation by decay heat. Therefore, it is of key importance to continuously supply water into a debris bed, which is affected by the pressure drop depending on the characteristics of debris bed such as bed porosity, particle morphology, particle size distribution, etc. Thus, in the present work, the influence of particle size distribution and the adequacy of mean diameters for predicting pressure gradients in particle beds were evaluated. Experimental data were obtained on the pressure gradients of air flow in packed beds composed of either spherical or cylindrical stainless steel particles having a size distribution of 1-10 mm. The results were compared with the values calculated by a proposed model in our previous work. When the area mean diameter was adopted as the effective particle diameter, the measured pressure gradients of air flow through each spherical particle bed with a particular size distribution agreed with the calculated values within a mean absolute percentage deviation of 9%. For a cylindrical particle bed with a particular size distribution, the measured pressure gradients agreed with the calculated values within a mean absolute percentage deviation of 12% when adopting the area mean diameter calculated using the equivalent diameter, the product of the Sauter diameter and particle shape factor as the effective diameter for non-spherical particles. This selection of mean and effective diameters produced the best fit among several candidates. Thus, we propose the area mean diameter (calculated using the equivalent diameter) as the effective diameter for determining the hydraulic diameter affecting fluid resistance in porous beds composed of non-spherical particles with a particular size distribution.