NONLINEAR INTERFACIAL INSTABILITY OF SEPARATED FLOW

Instability of the interface for two phase pipe flow and transition from stratified flow to slug or annular flow is considered a long wave phenomenon. Kelvin-Helmholtz (KH) analysis is usually used for analyzing the stability of the interface. Two types of linear stability analyses have been used (1) the inviscid Kelvin-Helmholtz analysis (IKH) in which the effect of the shear stresses on the stability is neglected and the viscous Kelvin-Helmholtz analysis (VKH) in which the shear stresses are considered. Interpretation of the linear analyses, with the help of experimental observation, shows that considerable information can be inferred from the linear analyses. Yet, the linear analysis is not sufficient, since the behavior beyond the linear approximation is just a logical speculation rather than a true predictive method. In this work the evolution of finite disturbances is studied by numerical simulations of the wave growth or decay using the method of characteristics. Three basic behaviors are identified: (1) the waves decay with time; (2) the wave amplitude grows until conditions of ill posedness at the wave crest is achieved and (3) the wave grows but the shape of the wave is distorted and develops steep slopes that lead to wave break. Case (1) is associated with stable stratified flow. Case (2) is associated with physical conditions where unbounded growth of the disturbances occur. This growth leads to transition to slug flow for low void fraction (h/D > 0.5) and annular flow for high void fraction (h/D < 0.5). Case (3) is associated with a wavy interface. The present results used to predict the transition from stratified flow boundaries are usually quite close to the results obtained from the linear theory (where interpretation of the non-linear behavior is speculated).