Accurate characterization of bubble mixing uniformity in a circular region using computational geometric theory

The present study proposes a novel method based on the geometric theory for measuring the distribution of bubble swarms in the circular region of a direct-contact heat exchanger. It was determined that the mixing is uniform when the average distance between the bubble swarms in the unit circular region is approximately 0.9054, which is the standard reference value. The effect of sample size (i.e., the number of bubbles) on mixing uniformity was investigated to determine the optimal sample size. It was verified that the metric's accuracy and stability were higher with a sample size of 155. Accordingly, it was proposed to increase the sample size by filling irregular bubbles using a segmentation method, which enabled a further accurate assessment of the mixing uniformity. The mixing uniformity of bubble swarms in the circular region and its maximum internal connection with the square region was accurately quantified. It was revealed that the relative average error increased by approximately 3.47% due to information loss. The proposed method was demonstrated to be rotationally invariant. The present study provided novel insights into evaluating mixing uniformity, which would guide enhanced heat transfer and the effective evaluation of the spatiotemporal characteristics of transient mixing in circular regions or the cross-sections of chemical transport pipelines.