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<p>The ascent of a toroidal air&#xa0;bubble in water was experimentally investigated using shadowgraphy and PIV. The bubble was generated by injecting a pulsed air jet vertically upwards into water. The bubble volume and its formation conditions were varied. The dependencies of the effective radius and ascent velocity on the elevation height were determined, and the trajectory of the bubble’s core center was constructed. Based on the analysis of the&#xa0;velocity field and geometric parameters, the circulation and the bubble expansion coefficient were calculated. The Froude number, based on circulation and characteristic bubble size, was&#xa0;found to scatter randomly about a mean value. It was&#xa0;established that the trajectory and the expansion coefficient of the toroidal bubble do not depend on the volume but are related to the value of the Froude number. An empirical dependence of the expansion coefficient on the Froude number was obtained, which is approximately inversely proportional to the Froude number, in qualitative agreement with the theory of self-similar buoyant vortices.</p>

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Similarity criteria for ascending toroidal bubbles in water

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Viktor Nikulin,
  • Evgeny Chashnikov

摘要

The ascent of a toroidal air bubble in water was experimentally investigated using shadowgraphy and PIV. The bubble was generated by injecting a pulsed air jet vertically upwards into water. The bubble volume and its formation conditions were varied. The dependencies of the effective radius and ascent velocity on the elevation height were determined, and the trajectory of the bubble’s core center was constructed. Based on the analysis of the velocity field and geometric parameters, the circulation and the bubble expansion coefficient were calculated. The Froude number, based on circulation and characteristic bubble size, was found to scatter randomly about a mean value. It was established that the trajectory and the expansion coefficient of the toroidal bubble do not depend on the volume but are related to the value of the Froude number. An empirical dependence of the expansion coefficient on the Froude number was obtained, which is approximately inversely proportional to the Froude number, in qualitative agreement with the theory of self-similar buoyant vortices.