Combustion of Liquefying Hybrid Propellants: Part 2, Stability of Liquid Films

Abstract

The stability of a liquid layer under strong blowing and subjected to large shear forces is investigated. This case is of practical importance for application to theregression rate estimation of liquefying hybrid rocket fuels such as solid cryogenichybrids. An Orr ‐Sommerfeld equation forthelinearstability of the liquid ‐gas interface is derived, and an exact solution is found for a linear base velocity proe le. The exact solution for the liquid phase is coupled with thelinearized gas-phase response with appropriate boundary conditions at the interfaceto give an eigenvalue problem for the linear stability of the layer. The results for liquid layer Reynolds numbers of practical interest (50‐300) show the existence of a range of unstable wave numbers. It is observed that both the most amplie ed wave number and the maximum amplie cation increases with the liquid Reynolds number. It is also discovered that increasing surface tension and liquid viscosity have a stabilizing effect on the e lm. This prediction is supported by experimental results showing fast burning rates for low-viscosity fuels such as solid cryogenic pentane and noncryogenicwax. Finally, thestability theory is applied to the classical polymeric hybrid propellants that burn by forming a melt layer. Because the melt layers of these polymeric materials are highly viscous, they can not sustain thin e lm instabilities.