The mixing performances of side-blown gas jets were studied by characterizing their manifold Betti numbers, namely 0-dimensional and 1-dimensional Betti numbers, through flow visualization and image processing techniques. The 0-dimensional Betti number reflects the mixing performance, and the 1-dimensional Betti number reflects the mixing unevenness degree. The mixing performances and flow fields were studied for different modified Froude numbers. As modified Froude numbers increase, the main flow was enhanced, promoting the macro-mixing of individual particles. The mixing performance of the stirring process was improved by a frequency conversion method, which destroyed the original flow pattern and promoted the micro-mixing process by chaotization.
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