Simple Lagrangian formulation of bubbly flow in a turbulent boundary layer (bubbly boundary layer flow)

• Published in: Journal of marine science and technology Vol. 2; no. 1; pp. 1 - 11
• Main Authors: Yoshida, Yuki, Takahashi, Yoshiaki, Kato, Hiroharu, Masuko, Akira, Watanabe, Osamu
• Format: Journal Article
• Language: English
• Published: Tokyo Springer Nature B.V 01.03.1997
• Subjects: Aircraft; Boundary layer; Boundary layers; Bubbles; Cavitation; Flow channels; Fluid flow; Friction; Injection; Liquid phases; Marine; Mathematical analysis; Mathematical models; Shear stress; Skin friction; Turbulent boundary layer; Turbulent flow
• ISSN: 0948-4280; 1437-8213
• DOI: 10.1007/BF01245932

For the theoretical consideration of a system for reducing skin friction, a mathematical model was derived to represent, in a two-phase field, the effect on skin friction of the injection of micro air bubbles into the turbulent boundary layer of a liquid stream. Based on the Lagrangian method, the equation of motion governing a single bubble was derived. The random motion of bubbles in a field initially devoid of bubbles was then traced in three dimensions to estimate void fraction distributions across sections of the flow channel, and to determine local bubble behavior. The liquid phase was modeled on the principle of mixing length. Assuming that the force exerted on the liquid phase was equal to the fluid drag generated by bubble slip, an equation was derived to express the reduction in turbulent shear stress. Corroborating experimental data were obtained from tests using a cavitation tunnel equipped with a slit in the ceiling from which bubbly water was injected. The measurement data provided qualitative substantiation of the trend shown by the calculated results with regard to the skin friction ratio between cases with and without bubble injection as function of the distance downstream from the point of bubble injection.