A probability model for churn flow in vertical pipes: Predicting the distribution of disturbance wave scale and void fraction

As a complex flow state in vertical transportation pipelines, churn flow is crucial for optimizing industrial pipeline design and improving fluid transportation efficiency. This study develops a probabilistic analysis model to explore the dynamic characteristics of churn flow in vertical pipelines and its impacts on gas-liquid two-phase flow. Interfacial waves, a key feature in two-phase flow, are essential for flow state conversion and influencing heat and mass transfer processes. The model, based on dynamic equilibrium, examines the generation and dissipation of interfacial fluctuations, treating the influence of vortices on the liquid film as a Markov process. This approach allows for the statistical stabilization of churn flow under specific conditions, facilitating predictions of liquid film thickness and void fraction. These predictions consider variables such as fluid flow rate, pipe size, and fluid physical properties, with accuracy and applicability validated through experimental data. The present study also investigates the effects of gas and liquid velocities, liquid density, liquid viscosity, liquid surface tension, and pipe diameter on the liquid film thickness and the void fraction. The sensitivity analysis reveals that the pipe diameter significantly influences the liquid film thickness, the flow field is more sensitive to the gas velocity than the liquid velocity, and the liquid density notably affects both the liquid film thickness and the void fraction.