On the structure of nonlinear waves in liquids with gas bubbles

Abstract

Transient wave phenomena in two-phase mixtures with a liquid as the matrix and gas bubbles as the dispersed phase have been studied in a shock tube using glycerine as the liquid and He, N2, and SF6 as gases having a large variation in the ratio of specific heats and the thermal diffusivity. Two different sizes of bubble radii have been produced , R0=1.15 and 1.6 mm, with a dispersion in size of less than 5%. The void fraction was varied over one order of magnitude, φ0=0.2%–2%. The measured pressure profiles were averaged by superimposing many shots, typically 20. Speeds and profiles were measured for shock waves and for wave packets. Investigation of the wave structure allows one to approach the fundamental question of how the physics on the level of the microstructure influences the behavior on the macroscale. In the theoretical work, modeling on the basis of a hierarchy of characteristic length scales is developed. Bubble interactions, transient heat transfer, and dissipation due to molecular and bulk viscosities are included. Solutions for small void fractions and moderate amplitudes are obtained for the steady cases of shock waves and solitons and are compared with the experimental results.

Direct and Homogeneous Numerical Approaches to Multiphase Flows and Applications

“…The shock speeds agreed with the theoretical prediction of [13] very well (with the difference less than 3%). The shock profiles agreed with experiments of Beylich and Gulhan [1] qualitatively and partly quantitatively. Some discrepancy in the amplitude of pressure oscillations can be explained by grid related numerical errors.…”

“…Significant progress has been achieved using various homogeneous descriptions of multiphase systems (see for example [1,2,13,15] and references therein). The Rayleigh-Plesset equation for the evolution of the average bubble size distribution has often been used as a dynamic closure for fluid dynamics equations.…”

Shock propagation through a bubbly liquid in a deformable tube

“…The shock theory has been validated by experiments (Campbell & Pitcher 1958;Noordzij & van Wijngaarden 1974;Beylich & Gülhan 1990;Kameda & Matsumoto 1996;Kameda et al 1998). In these experiments, bubbly mixtures were created in a tube, but the shock pressure was small enough to minimize the FSI effect.…”

Shock Propagation in Polydisperse Bubbly Liquids

“…If the distribution is sufficiently broad (say, σ = 0.7), the shock profile is smoothed out, indicating the quasistatic behavior of a polydisperse bubble cloud in spite of individual bubble dynamics. Such a smoothed shock profile in a polydisperse mixture is reported in the experiment of Beylich and G¨ulhan [11].…”

“…In the pioneering work of Campbell and Pitcher [20] and the subsequent experiments (see for example [11,44,45,60,79]), dispersed bubbly flows were created in a vertical tube attached to a shock tube in order to generate shock propagation. Shocks in monodisperse bubbly flows exhibit an oscillatory structure that can also be numerically predicted using continuum models coupled with single-bubble-dynamic equations [44,45,58,70,78,87].…”