VIII-7

L. van Wijngaarden, J. M. Burgers

University of Twente

Abstract

Perturbations of void fraction can propagate through a disperse gas/liquid flow. Accompanied by pressure perturbations they are called sound waves or pressure waves. If pressure perturbations are negligible and there are, apart from disturbances of the gas concentration, only velocity perturbations, they are called voidage or concentration waves. In this contribution the present understanding of both type of waves is discussed, from the point of view of the author, who reviewed these at earlier occasions (van Wijngaarden, 1972, 1988). Since then, progress has been made concerning these waves. Regarding sound waves there is a better understanding of the thermal aspects, leading to more insight in the damping or attenuation of pressure waves. Questions, raised by Watanabe & Prosperetti (1994) concerning the behavior of shock waves in bubbly flows, has been satisfactorily settled. Also here, the transfer of thermal energy from bubbles to liquid plays an important part. Regarding voidage waves, there is less encouraging news. How a mixture of liquid and stably rising bubbles, easily producible in the laboratory, is possible, is still not understood theoretically. Once such a mixture is assumed, voidage waves can be predicted theoretically, the predictions begin in very good agreement with observation (Lammers & Biesheuvel 1996). For a long time it has been believed that transition to plug flow is caused by instability of void waves. After much research effort, there seems to be no firm support for this view. On the other hand, voidage waves do become unstable. In how far this instability has to do with transition to other regions of the flow map, remains to be resolved. These and other aspects of waves in bubbly flows are discussed.

Watanabe, M. & Prosperetti, A. 1994, Shock waves in dilute bubbly liquids, J. Fluid Mech. 274, 349-381.

Wijngaarden, L. van, 1972, One-dimensional flow of liquids containing small air bubbles, Ann. Rev. Fluid Mech 4, 369-396

Wingaarden, L van, 1988, Flow of bubbly liquids, In Theoretical and Applied Mechanics, Proc. of the 17th International Congress of Theoretical & Applied Mechanics, Ed. P. Germain, M. Piau and D. Caillerie.