Stability Analysis and Direct Numerical Simulation for Two-Phase Flows and Heat Transfer: A Complementary Approach

In this chapter, we develop the theory of linear stability analysis for two-phase stratified flows. This is used to explain the origin of waves on an otherwise flat interface. We apply the theory to several model flows, in particular channel flows where the base, state is either laminar or turbulent. The theory applies only to situations where the waves have an infinitesimally small amplitude. If the waves grow over time (corresponding to instability), the theory eventually ceases to be valid. In certain scenarios, it may be possible to extend the theory via weakly nonlinear analysis — this is explored below. However, to obtain a full picture of the eventual fate of the interfacial waves, direct numerical simulation of the full two-phase Navier–Stokes equations is required. This complementary methodology is also developed, and results of the two approaches are compared and contrasted for several model flows of industrial relevance.