A mechanistic investigation of nonlinear interfacial instabilities leading to slug formation in multiphase flows

Abstract

Many industrial applications involve the transport of multiphase flows through pipes. For instance, the design and operation of oil pipelines and production facilities relies heavily on understanding the hydrodynamics of inultiphase flow. Industrial engineers utilizes multiphase flow simulators to aid in the design and flow assurance of such systems; however, the complexity of the physics and the range of scales involved in the problem require that the numerical algorithms invoke phase averaging methods and rely on empirical models. These assumptions and simplifications often result in predictions which are non-physical or are off by orders of magnitude forcing engineers to implement conservative safety factors to accommodate the large uncertainties. The development of physics based models may reduce the empiricism in the simulators allowing for the creation of more robust and cost effective designs. The work described in this thesis carries out both theoretical and computational investigations of some nonlinear mechanisms governing the interfacial stability and nonlinear evolution of stratified two-phase flows through horizontal channels and pipes. The resulting investigation identifies a strong nonlinear energy transfer mechanism which extracts energy generated by an interfacial instability and transfers it (with possible bi-exponential growth rates) to long wavelength waves which may eventually evolve into large amplitude waves and slugs. Detailed investigations demonstrate the effectiveness of this mechanism in flows ranging from ideal (potential) to turbulent two-phase flows. This thesis consists of three key focus areas. The first section develops a nonlinear potential flow analysis to identify a mechanism composed of a triad of resonantly interacting interfacial waves which are influenced by the Kelvin-Helmholtz interfacial instability. The mechanism that is identified permits the rapid energy transfer from linearly unstable short waves to stable long waves through nonlinear resonant wave interactions. It was found that, depending on the flow conditions, it is possible for linearly stable waves to achieve bi-exponential growth due to the resonant coupling. Extensions of this mechanism to broadbanded wave interactions were found to be in close agreement with experimental measurements. The analysis was also adjusted to examine the special case of sub-harmonic resonant interactions which have been observed in many experimental measurements and it was shown that this special case could still effectively create rapid long wave growth with up to bi-exponential growth rates. The second focus area examines the robustness of the aforementioned potential flow mechanism by identifying if a linear interfacial instability could be effectively coupled with resonant interactions in the presence of viscosity and flow turbulence. Using a linear stability analysis along with direct numerical simulations, comparisons were made against experimental measurements. This analysis was able to accurately identify the bandwidth of unstable interfacial modes as well as predict the existence of the strong sub-harmonic and triad resonances among modes which were reported in the experimental observations. The behavior observed in the numerical simulations demonstrates that the coupled instability-resonance mechanism is capable of existing in more complex two-phase turbulent flows and still permits the rapid exchange of energy from unstable short to linearly stable long wavelength modes. In addition, the numerical simulation results provide high-resolution data sets for which the interfacial stress distributions could quantified and described providing insights into the necessary behavior of future interfacial stress modeling. The final focus area is dedicated to developing a novel nonlinear slug transition criterion which couples the effects of a linear instability with that of nonlinear resonant interaction theory. An energy bounding condition is proposed for which the number of resonant modes which are linearly unstable is minimized allowing for a critical gas velocity to be identified. Comparisons are made against experiments carried out in horizontal channels and good agreement is observed. A heuristic method is proposed which allows for "equivalent" channel flow conditions to be obtained which are representative of the original pipe flow conditions. Unlike previously developed slug transition conditions, this new nonlinear criterion provides predictions which are significantly more accurate when compared against experimental measurements and maintains its accuracy over a large range of pipe diameters, flow conditions, and fluid combinations.