Euler–Lagrange study of bubble breakup and coalescence in a turbulent boundary layer for bubble drag reduction

Abstract

By injecting bubbles on the surface of ships or underwater vehicles, friction resistance can be effectively reduced. This technique is known as bubble drag reduction (BDR). The Euler–Lagrange method has been proved to be an effective numerical method in the study of the BDR mechanism. Bubble diameters were uniform in previous Euler–Lagrange simulations. However, many experimental results indicated that there is a nonuniform bubble size distribution under the action of turbulence, which affects the drag reduction significantly. In this paper, the authors developed a Euler–Lagrange code with the ability to simulate bubble breakup and bubble coalescence. The process of BDR on a flat plate is simulated by injecting bubbles into a turbulent boundary layer flow. Diameters of the bubbles are the same when they are injected into the flow field. During the simulation, bubbles of varying sizes can be clearly simulated in the evolution process due to breakup and coalescence. The drag reduction effect and bubble size distribution are validated by comparison with previous experimental data. Numerical results with and without breakup and coalescence models are discussed in detail to illustrate the advantage of the present algorithm. Moreover, bubble size distribution, bubble trajectory, and bubble induced turbulent modulation are analyzed in detail to explain the mechanism and its relationship with bubble size distribution.