AI summaryⓘ
The authors study churn flow, a chaotic pattern that happens in vertical air-water flow but has lacked a clear mathematical definition for decades. They use a new method based on topology, analyzing the shape and connectivity of flow patterns through Euler Characteristic Surfaces (ECS). Their approach combines topological features with flow speed data to identify different flow regimes without any labeled examples, achieving high accuracy. They also validate their findings across multiple data sets and show their method corrects previous models that underestimated churn flow behavior in small pipes. This work offers the first precise math-based way to define churn flow and shows unsupervised learning can reveal important flow characteristics.
Churn flowTwo-phase flowEuler Characteristic SurfacesTopologyMultiple Kernel LearningUnsupervised learningSlug flowGas velocityFlow regime transitionInterfacial tension
Authors
Brady Koenig, Sushovan Majhi, Atish Mitra, Abigail Stein, Burt Todd
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.