Using an Effective Viscosity to Account for the Effect of the Walls on the Pressure Drop Through an Annular Packed Bed

The question arose whether the correlation for the pressure drop prescribed for cylindrical pebble bed reactors by the Nuclear Safety Commission (KTA) of Germany could still be applied to the proposed annular configuration of the Pebble Bed Modular Reactor (PBMR) currently being developed in South Africa. An approach is described which uses the extended Brinkman equation for fully developed flow together with the original KTA correlation, to account for the resistance of the pebbles, and an effective viscosity, to account for the effect of the walls. A cylindrical packed bed with the same hydraulic diameter as the annular core was first of all considered. The pressure drops for various Reynolds numbers were calculated using a correlation which accounts for the effect of the wall. The formulation of the correlation for an infinite bed was then used along with the Brinkman equation to determine the appropriate values of the effective viscosity to give the same pressure drops. It was then assumed that the effective viscosities obtained in this way could be applied to the annular configuration of the PBMR. The pressure drop through the annular core was then calculated for various Reynolds numbers employing the effective viscosities in the extended Brinkman equation. It was found that the friction coefficients that could be derived from these pressure drops were in good agreement with the friction coefficients obtained from physical experiments performed on a scale model of the PBMR annular core. It was therefore concluded that the strategy followed could be used with the necessary care to predict the pressure drop through the annular core of the PBMR.