A novel approach for measuring bubbles uniformity and mixing efficiency in a direct contact heat exchanger

Measure of bubble non-uniformity within circular region in a direct-contact heat exchanger

“…It is also seen from the top of Fig.2 that the points are scattered quite uniformly. However, a faulty judgment was obtained by the previous method reported in the literature (Fei et al, 2015) obviously. Studying carefully its reason, it is immediately clear from Eq.2 that the star discrepancy is only applicable to rectangular region Ω.…”

“…Furthermore, the bubble uniformity and mixing efficiency are quantities related to the direct-contact heat transfer coefficient in the light of computational homology [5]. It was found that the direct-contact heat transfer performance was not only about the number of bubble swarms which could be characterized by Betti numbers, but it was all about the spatial-time location of bubble swarms because aggregate was considered to be related to the specific surface area [6]. Mixing must satisfy not only the needs of mass and heat transfer but also the required homogeneity in the vessel in the shortest time 1 These authors have contributed equally to this work.…”

“…The critical point determination of pseudo homogeneous process impact on the accurate estimation of mixing time could be investigated by three-sigma (3σ) method [2]. Fei et al (2015) and addressed the key issue that how to measure the spacetime uniformity of random bubble swarm in a domain with minimum discrepancy [6,21]. S 2 , a more meaningful parameter, was also represented to study the mixing transient [22].…”

“…It is widely used in multivariate integration, pseudorandom number generation, statistics, and computer graphics. Particularly, regarding the measure of distribution uniformity of bubble swarm in direct-contact boiling heat transfer process, it is common practice to quantify the bubble swarm in rectangle region [6,21,22]. However, the patterns were imaged through a circular viewing window from where we could observe the most active stage of the bubbling regime in the bubble evaporation process.…”

Quantifying the evolution of flow boiling bubbles by statistical testing and image analysis: toward a general model

“…In terms of the bubbling regimes in direct contact heat exchanger (DCHE), Betti numbers can be used to estimate the number of bubbles aggregating in flow patterns and to obtain the pseudo-homogeneous time 5 . We concluded that bubble swarm images can be captured and processed advantageously due to image enhancement technology and mathematical methods 6 .…”