Topological Characterization of Churn Flow and Unsupervised Correction to the Wu Flow-Regime Map in Small-Diameter Vertical Pipes

2026-04-07

AI Summary

This study addresses the lack of a quantitative mathematical definition for churn flow in small-diameter gas–liquid two-phase systems and the systematic underestimation of its onset by existing flow pattern maps. To resolve this, the work proposes a novel topological characterization based on the Euler characteristic surface (ECS) and develops an unsupervised multi-kernel learning framework that integrates time-aligned and amplitude-statistical features derived from ECS with gas velocity information to enable self-calibrated flow regime identification. Evaluated on the Montana Tech dataset, the method demonstrates that topological features contribute 64% to classification performance and reveals that the transition velocity from churn to slug flow is 3.81 m/s higher than predicted by the Wu model. On the TAMU dataset, it achieves 95.6% accuracy across four flow regimes and 100% recall for churn flow, significantly outperforming supervised approaches that rely heavily on labeled data.

Abstract

Churn flow-the chaotic, oscillatory regime in vertical two-phase flow-has lacked a quantitative mathematical definition for over $40$ years. We introduce the first topology-based characterization using Euler Characteristic Surfaces (ECS). We formulate unsupervised regime discovery as Multiple Kernel Learning (MKL), blending two complementary ECS-derived kernels-temporal alignment ($L^1$ distance on the $χ(s,t)$ surface) and amplitude statistics (scale-wise mean, standard deviation, max, min)-with gas velocity. Applied to $37$ unlabeled air-water trials from Montana Tech, the self-calibrating framework learns weights $β_{ECS}=0.14$, $β_{amp}=0.50$, $β_{ugs}=0.36$, placing $64\%$ of total weight on topology-derived features ($β_{ECS} + β_{amp}$). The ECS-inferred slug/churn transition lies $+3.81$ m/s above Wu et al.'s (2017) prediction in $2$-in. tubing, quantifying reports that existing models under-predict slug persistence in small-diameter pipes where interfacial tension and wall-to-wall interactions dominate flow. Cross-facility validation on $947$ Texas A&M University images confirms $1.9\times$ higher topological complexity in churn vs. slug ($p < 10^{-5}$). Applied to $45$ TAMU pseudo-trials, the same unsupervised framework achieves $95.6\%$ $4$-class accuracy and $100\%$ churn recall-without any labeled training data-matching or exceeding supervised baselines that require thousands of annotated examples. This work provides the first mathematical definition of churn flow and demonstrates that unsupervised topological descriptors can challenge and correct widely adopted mechanistic models.

Problem

• churn flow
• flow regime map
• topological characterization
• two-phase flow
• unsupervised learning

Innovation

• Euler Characteristic Surfaces
• Multiple Kernel Learning
• unsupervised flow regime identification
• churn flow characterization
• topological data analysis