A theoretical model with variable masses for the molten fuel-sodium thermal interaction in a nuclear fast reactor

In the model proposed in this paper, the reaction has been asumed to occur in two successive phases, A and B.

1. Phase A. A given number (function of time) of fuel particles come into intimate contact with a given mass of liquid sodium (function of time). The heat transfer process is characterized by good direct thermal contact between the fuel and the liquid coolant, and by a large contact area due to the small size of the particles. The heat transfer coefficient decreases with time due to the formation of a temperature profile inside the fuel particles. The heated volume of sodium is constrained by the surrounding unheated coolant and by the other materials present in the core. The mechanical constraint is schematized by a sodium column of finite length which is contained in a channel located above the reaction volume. The sudden expansion of the heated volume first produces acoustic waves which travel along the sodium column. Later the sodium column behaves like a piston which is pushed inertially upwards. The pressure rises, reaches a maximum, and then falls as soon as the expansion of the liquid sodium becomes inportant. At the time at which the pressure reaches the saturation point, sodium boiling starts and phase B begins.

2. Phase B. The heat transfer process is now characterized by a very large contact area, and by thermal contact between the fuel and coolant which becomes increasingly worse with time, due to the formation of a sodium vapour layer at the external surface of the fuel fragments. The sodium will boil in a large quantity, and will therefore produce large volume changes. The sodium piston will be further accelerated and its movement will allow the pressure in the reaction volume to decrease.

The model accounts for the time history of the temperatures of each fuel particle by means of the use of specially averaged temperature values. The calculation of the heat transfer coefficient during phase B is based on experimental results. The presence of fission gases can also be taken into account. A size distribution of fuel particles has also been incorporated into the model as well as the effect of friction due to the channel walls and that of the pressure losses at the outlet of the channel. Numerical evaluations are also included and the results are discussed. It has been concluded that the total work produced decreases with the time scale of the vapour film layer around the particles and increases with the speed at which the fuel breaks down into fragments and mixes with the liquid sodium. The effect of sodium column length has also been investigated.