### Abstract

The collapse of a spherical cavitation bubble contained in a large body of upper convected Maxwell fluid is theoretically analyzed by using a variational principle approach in the Lagrangian frame for the K-BKZ rheological equation of state with potential functions. Based on the Rayleigh time scale for bubble collapse in ideal fluids, two parameters. Re and De, are identified. Using a finite element technique, a fully explicit numerical scheme is developed both for the pressure distribution calculation and for bubble surface tracking. The same problem is formulated also using the Galerkin-finite element method in the Lagrangian frame for the differential model of an upper convected Maxwell fluid. With the latter method, the viscoelastic stress can be determined explicitly. Even though the result is the same as far as the radius-time curve is concerned, each method has its own advantages. Highly oscillatory behaviors in bubble radius are observed for moderate Re and De. For large ReDe, the solution exhibits an asymptotic behavior. It is also observed that fluid elasticity accelerates the collapse in the early stage of collapse while in the later stages it retards the collapse. The retardation for a moderate range of Re is expected to be related to the reduced cavitation damage in viscoelastic fluids.

Original language | English |
---|---|

Pages (from-to) | 37-58 |

Number of pages | 22 |

Journal | Journal of Non-Newtonian Fluid Mechanics |

Volume | 55 |

Issue number | 1 |

Publication status | Published - 1994 Oct 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cavitation
- Cavitation damage
- Drag reducing fluid
- Elasticity
- Lagrangian frame
- Rebound

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes

### Cite this

*Journal of Non-Newtonian Fluid Mechanics*,

*55*(1), 37-58.

**Collapse of spherical bubbles in Maxwell fluids.** / Kim, Chongyoup.

Research output: Contribution to journal › Article

*Journal of Non-Newtonian Fluid Mechanics*, vol. 55, no. 1, pp. 37-58.

}

TY - JOUR

T1 - Collapse of spherical bubbles in Maxwell fluids

AU - Kim, Chongyoup

PY - 1994/10/1

Y1 - 1994/10/1

N2 - The collapse of a spherical cavitation bubble contained in a large body of upper convected Maxwell fluid is theoretically analyzed by using a variational principle approach in the Lagrangian frame for the K-BKZ rheological equation of state with potential functions. Based on the Rayleigh time scale for bubble collapse in ideal fluids, two parameters. Re and De, are identified. Using a finite element technique, a fully explicit numerical scheme is developed both for the pressure distribution calculation and for bubble surface tracking. The same problem is formulated also using the Galerkin-finite element method in the Lagrangian frame for the differential model of an upper convected Maxwell fluid. With the latter method, the viscoelastic stress can be determined explicitly. Even though the result is the same as far as the radius-time curve is concerned, each method has its own advantages. Highly oscillatory behaviors in bubble radius are observed for moderate Re and De. For large ReDe, the solution exhibits an asymptotic behavior. It is also observed that fluid elasticity accelerates the collapse in the early stage of collapse while in the later stages it retards the collapse. The retardation for a moderate range of Re is expected to be related to the reduced cavitation damage in viscoelastic fluids.

AB - The collapse of a spherical cavitation bubble contained in a large body of upper convected Maxwell fluid is theoretically analyzed by using a variational principle approach in the Lagrangian frame for the K-BKZ rheological equation of state with potential functions. Based on the Rayleigh time scale for bubble collapse in ideal fluids, two parameters. Re and De, are identified. Using a finite element technique, a fully explicit numerical scheme is developed both for the pressure distribution calculation and for bubble surface tracking. The same problem is formulated also using the Galerkin-finite element method in the Lagrangian frame for the differential model of an upper convected Maxwell fluid. With the latter method, the viscoelastic stress can be determined explicitly. Even though the result is the same as far as the radius-time curve is concerned, each method has its own advantages. Highly oscillatory behaviors in bubble radius are observed for moderate Re and De. For large ReDe, the solution exhibits an asymptotic behavior. It is also observed that fluid elasticity accelerates the collapse in the early stage of collapse while in the later stages it retards the collapse. The retardation for a moderate range of Re is expected to be related to the reduced cavitation damage in viscoelastic fluids.

KW - Cavitation

KW - Cavitation damage

KW - Drag reducing fluid

KW - Elasticity

KW - Lagrangian frame

KW - Rebound

UR - http://www.scopus.com/inward/record.url?scp=0028524136&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028524136&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0028524136

VL - 55

SP - 37

EP - 58

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

IS - 1

ER -