Flow instability in particle-bed nuclear reactors

The particle-bed core offers mitigation of some of the problems of solid-core nuclear rocket reactors. Dividing the fuel elements into small spherical particles contained in a cylindrical bed through which the propellant flows radially, may reduce the thermal stress in the fuel elements, allowing higher propellant temperatures to be reached. The high temperature regions of the reactor are confined to the interior of cylindrical fuel assemblies, so most of the reactor can be relatively cool. This enables the use of structural and moderating materials which reduce the minimum critical size and mass of the reactor. One of the unresolved questions about this concept is whether the flow through the particle-bed will be well behaved, or will be subject to destructive flow instabilities. Most of the recent analyses of the stability of the particle-bed reactor have been extensions of the approach of Bussard and Delauer, where the bed is essentially treated as an array of parallel passages, so that the mass flow is continuous from inlet to outlet through any one passage. A more general three dimensional model of the bed is adopted, in which the fluid has mobility in three dimensions. Comparison of results of the earlier approach to the present one shows that the former does not accurately represent the stability at low Re. The more complete model presented should be capable of meeting this deficiency while accurately representing the effects of the cold and hot frits, and of heat conduction and radiation in the particle-bed. It can be extended to apply to the cylindrical geometry of particle-bed reactors without difficulty. From the exemplary calculations which were carried out, it can be concluded that a particle-bed without a cold frit would be subject to instability if operated at the high temperatures desired for nuclear rockets, and at power densities below about 4 megawatts per liter. Since the desired power density is about 40 megawatts per liter, it can be concluded that operation at design exit temperature but at reduced power could be hazardous for such a reactor. But the calculations also show that an appropriate cold frit could very likely cure the instability. More definite conclusions must await calculations for specific designs.