Analysis on Liquid-Vapor Bubbly-Flow Systems in Reciprocating Motion

An anuhʹtical study is performed on the dynamics and hydrodynamic stability of liquid-vapor mixtures in the huhhly-ftow range in reciprocating (notion through a horizontal channel. The perturbation technique is applied on the one-dimensional conservation equations for laminar flow and on the thermodynamic equation of state. The Laplace transform is operated on the linearized equations from which a transfer function is derived, relating the flow rate change due to a change in pressure drop along the channel. The resulting characteristic equation is analyzed to determine the dynamic behavior of the tVtʹo-phaseftow in reciprocating motion and the conditions for neutral stability under which self-induced oscillations occur. The natural frequency of the physical system is derived, which can be used to predict the resonance that will occur inforced vibrations. Results can be applied to systems such as car suspensions (shock absorbers) in which oil is susceptible to cavitation, resulting in bubbly flow due to vibrations. Conditions under which resonance occurs in the two-phase, system are determined. Resonance leads to severe oscillations and noise generation, as experienced inshock absorbers in car suspensions.