On the structure of shock waves in liquid-bubble mixtures

L. van Wijngaarden

Research output: Contribution to journalArticleAcademic

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Abstract

The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by the inertia of the radial flow associated with an expanding or compressed bubble. For not too thick shocks the dissipation by radial motion around the bubbles dominates over the dissipation by relative translational motion, in mixtures with low gas content. The overall thickness of the shock appears to be determined by the dispersion effect. Dissipation, however, is necessary to permit a steady shock wave. It is shown that, analogous to undular bores, a stationary wave train may exist behind the shock wave.
Original languageUndefined
Pages (from-to)366-381
JournalApplied scientific research
Volume22
Issue number1
DOIs
Publication statusPublished - 1970

Keywords

  • IR-85613

Cite this

van Wijngaarden, L. / On the structure of shock waves in liquid-bubble mixtures. In: Applied scientific research. 1970 ; Vol. 22, No. 1. pp. 366-381.
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On the structure of shock waves in liquid-bubble mixtures. / van Wijngaarden, L.

In: Applied scientific research, Vol. 22, No. 1, 1970, p. 366-381.

Research output: Contribution to journalArticleAcademic

TY - JOUR

T1 - On the structure of shock waves in liquid-bubble mixtures

AU - van Wijngaarden, L.

PY - 1970

Y1 - 1970

N2 - The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by the inertia of the radial flow associated with an expanding or compressed bubble. For not too thick shocks the dissipation by radial motion around the bubbles dominates over the dissipation by relative translational motion, in mixtures with low gas content. The overall thickness of the shock appears to be determined by the dispersion effect. Dissipation, however, is necessary to permit a steady shock wave. It is shown that, analogous to undular bores, a stationary wave train may exist behind the shock wave.

AB - The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by the inertia of the radial flow associated with an expanding or compressed bubble. For not too thick shocks the dissipation by radial motion around the bubbles dominates over the dissipation by relative translational motion, in mixtures with low gas content. The overall thickness of the shock appears to be determined by the dispersion effect. Dissipation, however, is necessary to permit a steady shock wave. It is shown that, analogous to undular bores, a stationary wave train may exist behind the shock wave.

KW - IR-85613

U2 - 10.1007/BF00400542

DO - 10.1007/BF00400542

M3 - Article

VL - 22

SP - 366

EP - 381

JO - Flow, turbulence and combustion

JF - Flow, turbulence and combustion

SN - 1386-6184

IS - 1

ER -