Bubble dynamics in a compressible
liquid with phase transition
Wolfgang Dreyer
Maren Hantke
Frank Duderstadt
Gerald Warnecke
WIAS Berlin
Otto-von-Guericke-University Magdeburg
Micro-Macro Modelling and Simulation of Liquid-Vapour Flows
Aachen, February 2009
A laser-induced cavitation bubble – experimental data
0.8
0.7
Radius in mm
0.6
0.5
0.4
0.3
0.2
0.1
0
0
Maren Hantke
10
20
30
40
50
Time in µs
60
70
Bubble dynamics in a compressible liquid with phase transition
80
90
100
Aachen, February 2009
First case
• The bubble consists of water vapour, hydrogen and oxygen.
• Homogeneity in the gas phase
• Ideal gas
• Incompressible liquid
• Isotherm process
Maren Hantke
Bubble dynamics in a compressible liquid with phase transition
Aachen, February 2009
Second case
• The bubble consists of water vapour, hydrogen and oxygen.
• Homogeneity in the gas phase
• Ideal gas
• Incompressible liquid
• Isotherm process
• Phase transition
Maren Hantke
Bubble dynamics in a compressible liquid with phase transition
Aachen, February 2009
Third case
• The bubble consists of water vapour, hydrogen and oxygen.
• Homogeneity in the gas phase
• Ideal gas
• Incompressible liquid
• Phase transition
• Heat conduction
Maren Hantke
Bubble dynamics in a compressible liquid with phase transition
Aachen, February 2009
Proposed model
• The bubble consists of water vapour, hydrogen and oxygen.
• Homogeneity in the gas phase
• Ideal gas
• Compressible liquid
• Phase transition
• Heat conduction
Maren Hantke
Bubble dynamics in a compressible liquid with phase transition
Aachen, February 2009
Numerical results
0.8
0.7
Radius in mm
0.6
0.5
0.4
0.3
0.2
0.1
0
0
Maren Hantke
20
40
60
80
Time in µs
100
Bubble dynamics in a compressible liquid with phase transition
120
140
Aachen, February 2009
Numerical results
0.6
0.4
0.2
20
40
60
80
Time in µs
100
500
800
600
400
20
40
60
80
100
120
20
40
60
80
100
120
Time in µs
0.025
−
0
−500
−1000
−1500
−2000
0
1000
200
0
120
Mass in 10 9kg
Liquid velocity in m/s
0
0
Maren Hantke
1200
Temperature in K
Radius in mm
0.8
20
40
60
80
Time in µs
100
120
0.02
0.015
0.01
0.005
0
Time in µs
Bubble dynamics in a compressible liquid with phase transition
Aachen, February 2009
Pressure wave
4 / 6 / 11.5 * 10^-6 s after collapse
6
2.5
x 10
Liquid pressure in Pa
2
1.5
1
0.5
0
0
0.005
0.01
0.015
0.02
0.025
Distance from origin in m
Maren Hantke
Bubble dynamics in a compressible liquid with phase transition
Aachen, February 2009
Effects we didn‘t take into account / Future work
• thermal extension
• oxygen dissolves in water
• higher order terms for compressibility
• wave propagation in the bubble
• reflecting boundary / velocity field in the beginning
• Multi bubble system
• System of balance laws for mixture theories
• Model non-conservative/production terms
• Pressure less gas model
Maren Hantke
Bubble dynamics in a compressible liquid with phase transition
Aachen, February 2009