Linear Instability of a Viscoelastic Planar Liquid Sheet in the Presence of Transverse Acoustic Field
In view of the possible acoustic oscillations in liquid rocket engines,the linear instability of the planar liquid film in the transverse acoustic field is analyzed theoretically.The momentum equation and boundary conditions of liquid film are described by the viscous potential flow theory.Based on Floquet theory,dispersion equation considering the coupling effect between the sinuous and varicose modes is obtained.The results show that there is a competitive relationship between the Kelvin-Helmholtz(K-H)instability caused by gas-liquid shear and the parameter instability caused by acoustic oscillaitons.The increase of Ohnesorge number,the decrease of elastic number and the increase of time constant ratio inhibits the instability of the liquid film.On one hand,the increase of Weber number weakens the surface tension and promotes the instability of liquid film.On the other hand,the increase of Weber number increases the wavenumber in the parameter instability region,which enhances the inhibition effect of viscosity on instability and inhibits the instability of liquid film.The increase of Bond number promotes parameter instability and inhibits K-H instability.With the increase of acoustic frequency,K-H instability is enhanced and parameter instability is weakened.