Abstract :
Additional conclusions are drawn regarding Goertzelʹs minimum mass flat-flux problem. In particular, we derive the basic integral equation for the fuel distribution required for a flat flux in the two group approximation for a reactor with a reflector of finite thickness. As noted by Goertzel, the general solution involves a continuously distributed component and an additional component in the form of a highly concentrated spike at the core–reflector interface. We have studied how the minimum mass varies as a function of reflector thickness and note that in the case where there is no spike then, over a limited range, the critical size can take the same value for two different reflector thicknesses. The critical masses are different for these two cases, the one with the smaller reflector thickness having the higher mass. We also show that, for any reactor thickness, there is a minimum value of reflector thickness below which criticality cannot be achieved with a flat flux. The results are illustrated numerically and graphically for graphite and water moderators.
