• Acta Physica Sinica
  • Vol. 69, Issue 18, 184703-1 (2020)
Xiang Li1, Yong Chen2、3、*, Hao Feng1, and Lei Qi4
Author Affiliations
  • 1School of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
  • 2College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
  • 3China Aerodynamics Research and Development Center, Mianyang 621000, China
  • 4Beijing Institute of Spacecraft Environment Engineering, Beijing 100094, China
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    DOI: 10.7498/aps.69.20200546 Cite this Article
    Xiang Li, Yong Chen, Hao Feng, Lei Qi. Axially-distributed bubble-bubble interaction under a coustic excitation in pipeline[J]. Acta Physica Sinica, 2020, 69(18): 184703-1 Copy Citation Text show less


    Acoustically-excited bubble dynamics is the foundation of pipeline bubble detection based on acoustic technology. Due to the existence of multiple bubbles in pipeline flow, the Bjerknes forces among arbitrary bubbles under acoustic excitation may enforce bubble-bubble interaction and then change the features of bubble dynamics. Based on traditional free bubble’s Rayleigh-Plesset (R-P) model, this paper tries to establish bubble-bubble interaction model in consideration of the second Bjerknes force and bubble distribution in the pipeline axial direction. Meanwhile, the influence of finite wave speed in compressible fluid is considered. The proposed model is numerically calculated by the fourth-order Runge-Kutta method. Firstly, the differences in bubble feature between the free bubble’s R-P model and bubble-bubble interaction model are compared under excitation with different frequencies and amplitudes. Results show that the differences in bubble dynamics are minor when the bubble’s distance is large enough. When the bubble’s distance is fixed, the differences are significant on condition that the frequency of acoustic excitation is nearly the resonant frequency of bubbles. Secondly, through establishing compressible model and incompressible fluid model, we compare the differences between the two models. Numerical calculations show that the second Bjerknes force under the compressible assumption acts as an external force and forces the bubble to vibrate. On the other hand, the second Bjerknes force under the incompressible assumption changes the dynamics of bubble-bubble interaction as well as the resonant features. Finally, we study the effect of bubble-bubble distance and bubble’s axial position on bubble vibration characteristics. The bubble-bubble distance affects the second Bjerknes force and may lead the bubbles to vibrate nonlinearly. The bubble’s axial position changes the phase of external acoustic force and leads to the difference in initial vibration feature. When this difference is coupled with the second Bjerknes force, the bubble-bubble interaction may be changed even into nonlinear vibration, leading the bubble’s oscillation spectrum to differ from linear vibrations significantly. These results demonstrate that the resonant state of a small bubble may be converted into nonlinear vibration state if the second Bjerknes force is present. On the other hand, the resonant state of a large bubble can keep linear vibration when the second Bjerknes force is not obvious.