Equations of Motion of a Liquid-Submerged Sonic Gas Jet Relative to Fission-Gas-Jet Impingement in Subassemblies of the Liquid Metal Fast Breeder Reactor

Abstract

It is well known that the small-perturbation equations governing steady or mildly unsteady potential flow in a sonic or a transonic gas jet are nonlinear. However, for a liquid-submerged sonic gas jet with a disturbance on the gas-liquid interface, the analysis shows that the unsteadiness introduced into the flow by oscillation of the gas-liquid interface due to presence of Kelvin-Helmholtz instability is sufficiently large, the nonlinear disturbance accumulation does not have time to develop, and the linearized treatment that includes the transient motion of gas becomes valid. Through an order-of-magnitude analysis of the full governing equations for the gas flow in a liquid-submerged axisymmetric sonic gas jet with a disturbance at the gas-liquid interface, the condition under which the governing equations can be linearized is obtained. It is shown that this condition of linearization takes the form of the Weber number (We) 26 (p/pg)0.2 for the case of low-viscosity liquids and We 36 for the high-viscosity liquids surrounding the gas jet. (Ug is the gas velocity, p is density, σ is surface tension, and p is the dynamic viscosity.) It is demonstrated that most gas-liquid systems of physical interest satisfy the condition of linearization. Examples of application can be found in the field of pneumatic atomization using a sonic gas jet, and in the field of Liquid Metal Fast Breeder Reactor (LMFBR) safety in relation to thermal transients induced by impingement on a fuel pin of a sonic fission-gas jet released from an adjacent breached pin. For the purpose of comparison with a sonic gas jet, it is also shown that in the case of subsonic and supersonic gas jets, the linearization of equations of motion to a first order is generally possible; that is, the condition of linearization for these jets is not as stringent as for the sonic gas jet. When in transient motion due to a disturbance at the gas-liquid interface having wave velocity much smaller than the gas velocity, the transient terms in comparison to perturbation terms of basic flow are of second order. In contrast to these jets, in the case of a sonic gas jet the transient motion of the gas cannot be neglected even at very slow oscillations of the gas-liquid interface.