Linear Stability Analysis of a Non-Newtonian Liquid Sheet

Abstract

Gel propellant is a non-Newtonian visco-elastic liquid. The study on breakup of a gel-propellant sheet emanated from an injector has always been a fundamental task for a propulsion system with gelled propellants. A linear instability analysis method has been used to investigate the breakup of a visco-elastic liquid sheet under the combined influence of sinuous and varicose modes of disturbances at the liquid-gas interfaces. The disturbance wave growth rate of two disturbance modes has been worked out by solving the dispersion equation of a visco-elastic liquid sheet, which is obtained by combining the linear instability theory and the linear visco-elastic model. The linear visco-elastic model can describe the thixotropic behavior of the visco-elastic fluid. Moreover, the maximum growth rate and corresponding dominant wave numbers have been observed. The surface deformation growth rate curves, maximum growth rate curves, and dominant wave numbers curves have been plotted. Also, the breakup time of the liquid sheet has been computed by plotting the surface deformation curves based on the surface deformation equation on the liquid-gas interfaces. The time constant ratio, zero shear viscosity, surface tension, liquid sheet velocity, liquid sheet thickness, gas-to-liquid density ratio, and liquid density have been tested for their influence on the instability of the visco-elastic liquid sheet. Furthermore, the instabilities of Newtonian fluid and visco-elastic fluid are compared with each other. The results show that the visco-elastic liquid sheet is more unstable than the Newtonian liquid sheet. Similarly, the sinuous mode disturbance is more unstable than the varicose mode.