Journal of Fluid Mechanics


Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water

C. K. TURANGANa1 p1, A. R. JAMALUDDINa1 p2, G. J. BALLa2 and T. G. LEIGHTONa3 c1

a1 School of Engineering Sciences, University of Southampton, Highfield, SO17 1BJ, UK

a2 Atomic Weapons Establishment, Aldermaston, Reading, RG7 4PR, UK

a3 Institute of Sound & Vibration Research, University of Southampton, Highfield, SO17 1BJ, UK


A free-Lagrange numerical method is implemented to simulate the axisymmetric jetting collapse of air bubbles in water. This is performed for both lithotripter shock-induced collapses of initially stable bubbles, and for free-running cases where the bubble initially contains an overpressure. The code is validated using two test problems (shock-induced bubble collapse using a step shock, and shock–water column interaction) and the results are compared to numerical and experimental results. For the free-running cases, simulations are conducted for a bubble of initial radius 0.3 mm located near a rigid boundary and near an aluminium layer (planar and notched surfaces). The simulations suggest that the boundary and its distance from the bubble influence the flow dynamics, inducing bubble elongation and jetting. They also indicate stress concentration in the aluminium and the likelihood of aluminium deformation associated with bubble collapse events. For the shock-induced collapse, a lithotripter shock, consisting of 56 MPa compressive and −10 MPa tensile waves, interacts with a bubble of initial radius 0.04 mm located in a free field (case 1) and near a rigid boundary (case 2). The interaction of the shock with the bubble causes it to involute and a liquid jet is formed that achieves a velocity exceeding 1.2 km s−1 for case 1 and 2.6 km s−1 for case 2. The impact of the jet on the downstream wall of the bubble generates a blast wave with peak overpressure exceeding 1 GPa and 1.75 GPa for cases 1 and 2, respectively. The results show that the simulation technique retains sharply resolved gas/liquid interfaces regardless of the degree of geometric deformation, and reveal details of the dynamics of bubble collapse. The effects of compressibility are included for both liquid and gas phases, whereas stress distributions can be predicted within elastic–plastic solid surfaces (both planar and notched) in proximity to cavitation events. There is a movie with the online version of the paper.

(Received November 26 2006)

(Revised September 20 2007)

Key words

  • Shock waves;
  • Bubble dynamics;
  • Cavitation


c1 Author to whom correspondence should be addressed:

p1 Present address: Institute of High Performance Computing, Singapore Science Park II, Singapore 117528.

p2 Present address: Romax Technology Limited, Nottingham Science & Technology Park, Nottingham, NG7 2PZ, UK.

Related Content