# A numerical framework for linear stability analysis of two-phase stratified pipe flows

## TL;DR

This paper introduces a novel numerical framework for linear stability analysis of two-phase stratified pipe flows, considering three-dimensional disturbances including interface effects, verified through Cartesian coordinate solutions, applicable to gas-liquid and liquid-liquid flows.

## Contribution

It presents the first comprehensive 3D stability analysis method for two-phase pipe flows using bipolar coordinates, enabling detailed interface and shear stress investigations.

## Key findings

- Validated bipolar coordinate method against Cartesian solutions.
- Analyzed stability of gas-liquid and liquid-liquid flows.
- Demonstrated detailed flow behavior near the interface and wall.

## Abstract

A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the interface between two fluids, are considered. The proposed numerical framework is based on a finite-volume method and allows solving the problem numerically in bipolar cylindrical coordinates. In these coordinates, both the pipe wall and the unperturbed interface (of a constant curvature, e.g., plane interface, as considered in this work) coincide with the coordinate surfaces. Thereby, the no-slip as well as the interfacial boundary conditions can be imposed easily. It also enables investigation of the local behavior of the flow field and shear stresses in the vicinity of the triple points, where the interface contacts the pipe wall. The results obtained in the bipolar coordinates are verified by an independent numerical solution based on the problem formulation in Cartesian coordinates, where the pipe wall is treated by the immersed boundary method. Two representative examples of gas-liquid and liquid-liquid flows are included to demonstrate the applicability of the proposed numerical technique for analyzing the flow stability.