Boiling Liquid Expanding Vapor Explosion and metastable behavior in 1D steady flow of liquids following a Clausius II equation of state

Boiling Liquid Expanding Vapor Explosion (BLEVE) is a rapid release of energy possible through the principle of metastability, a phenomenon that allows substances to retain a less stable (metastable) state, past the point of transition, up to a stability limit. Once this stability limit is reached the fluid can flash from a liquid to a vapor, resulting in an explosive release of energy. Cubic equations of state exhibit such regions of metastability and can be used for the explicit calculation of stability limits in non-equilibrium fluid systems. In this work, the Clausius-II equation of state is used to calculate thermodynamic properties in four simple one-dimensional steady-state steady-flow systems: a) frictional flow through a pipe; b) frictionless flow through an area variation; c) decelerating flow through a pipe; d) heat transfer through a pipe. The system of Euler equations of mass, inviscid momentum, and conduction-free energy are solved numerically in order to examine the propensity for BLEVE and capture its spatial structure in all four cases. The initial conditions and remaining flow parameters were chosen in such a way as to model approximately real-world accidents seen in nitrous oxide hybrid rocket systems. Results show that two out of the four non-equilibrium flow cases, namely flow with wall friction (Fanno) and flow with uniform deceleration, show increased propensity for metastable behavior as well as significant jumps in thermodynamic properties; at the same time the case involving area variation showed signs of metastable behavior only under unrealistically extreme conditions, while the case of uniform flow with heat transfer (Rayleigh) showed no metastable behavior.