The Role of Rayleigh-Taylor Instabilities in Fuel-Coolant Interactions

We investigate the growth of Rayleigh-Taylor instabilities following the deceleration of fuel by a less dense coolant using the method of generalized coordinates, which allows us to study the nonlinear, late-time aspects of the problem as well as the possibility of fuel freezing at the interface. We consider liquid coolant in contact with three possible states of fuel—pure liquid, pure solid, and liquid fuel freezing at the interface—and treat several acceleration mechanisms. Assuming the instability starts at a planar interface as a velocity perturbation proportional to the interfacial velocity, we find that when the fuel is completely frozen or freezing at the interface, instabilities will not grow unless the initial interfacial relative velocity satisfies a relationship of the form where υ₀ is the initial relative velocity, ρ_f the density of the fuel, Y₀ the yield strength of the frozen fuel, λ the wavelength of the instability, and L a characteristic length. The specific form of C depends on the acceleration mechanism and when freezing begins. For the case of UO₂ and sodium, we follow the growth of the fastest growing wavelength instability for different acceleration mechanisms and determine the impulse needed for instabilities to grow when freezing is occurring at the interface.