The Kelvin-Helmholtz/von Neumann Stability of Discrete Representations of the Two-Fluid Model for Stratified Two-Phase Flow

Many dynamic pipe flow simulator tools are capable of predicting the onset of hydrodynamic flow instability through detailed simulation. These instabilities provide a natural mechanism for flow regime transition. The quality and reliability of flow predictions are however strongly dependent upon the numerics within these simulator tools, the scheme type and resolution in particular. A Kelvin-Helmholtz stability analysis for the differential two-fluid model is in the present work presented and extended to discrete representations of said model. This analysis provides algebraic expressions which give instantaneous, quantitative information into i) when a studied scheme will predict linear wave growth, ii) the rate of growth and the expected growing wavelength, and iii) the wave speeds. These stability expressions adhere to a wider family of finite volume methods, directly applicable to any specific formulation within this group. Both the spatial and temporal discretization are found to play decisive roles in a method's predictive capability. Fundamental aspects of how numerical errors from the temporal integration affects the predicted stability are explored. Numerical errors are observed to manifest in increased, as well as reduced, wave growth. Low-frequency growth from numerical errors is not always easily distinguished from physical wave growth. The linear analysis is demonstrated to be useful in understanding the predictions made by simulator tools, and in choosing the appropriate numerical method and simulation parameters for optimizing the simulation efficiency and reliability.