Drag reduction by gas injection into turbulent boundary layer: Density ratio effect P.V. Skudarnov, C.X. Lin * Applied Research Center, Florida International University, 10555 W. Flagler St., EC 2100, Miami, FL 33174, USA Received 30 November 2004; received in revised form 21 November 2005 Available online 3 February 2006 Abstract A two-dimensional single phase computational fluid dynamics (CFD) model of microbubble-laden flow over a flat plate was used to assess the role of mixture density variation in microbubble drag reduction. The model consisted of Reynolds-averaged Navier–Stokes (RANS) transport equations, a standard k–x turbulence model, and a convection–diffusion species transport model. Performance of the model was validated with available experimental data and numerical simulations of more advanced multiphase two-fluid model. A parametric study of the density ratio effect on the drag reduction was carried out. The study indicated that simple mixture density variation effect plays one of the major roles in the microbubble drag reduction phenomenon. Also, the influence of the density ratio (the ratio of density of injected gas to that of water) on gas volume fraction profiles was found to be minimal within studied parameter range. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Microbubble drag reduction; Flat plate 1. Introduction The skin friction drag reduction has been a subject of extensive research during the past several decades. By reducing the skin friction drag an increased range or speed of the surface vessels, and underwater vehicles can be achieved. One of the methods to reduce the skin friction drag is gas injection into a liquid boundary layer, such injection results in the formation of microbubbles that pro- duces drag reduction. This technique is called microbubble drag reduction (MDR) and is able to provide drag reduc- tions of as much as 80%. MDR offers great potential in Naval applications. McCormick and Bhattacharya (1973) reported the first microbubble drag reduction experiments. During the past decades, many research efforts have been devoted to micro- bubble drag reduction (Merkle and Deutsch, 1992). The work conducted by researchers in the former Soviet Union and in the United States, primarily by the Applied Research Laboratory (ARL) at The Pennsylvania State University, provided the benchmark in microbubble drag reduction research. It has been found that there are many factors that influence microbubble drag reduction, includ- ing air jet flow rate, injection process, free stream velocity, pore size, buoyancy, and surface configuration. As evi- denced by published papers in the open literature, most of the previous studies of microbubble drag reduction were conducted experimentally. Due to the complexity of micro- bubble laden boundary layers, theoretical investigations have fallen behind the progress made by experimental stud- ies. It is recognized that a better understanding of the microbubble drag reduction mechanism is critical to its optimal performance with minimal use of gas volume in practical applications. In recent years, analytical computational modeling of microbubble drag reduction has been attempted by several researchers (Madavan et al., 1985; Marie, 1987; Kim and 0142-727X/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2005.12.002 * Corresponding author. Tel.: +1 305 348 1596; fax: +1 305 348 1852. E-mail address: chengxian.lin@arc.fiu.edu (C.X. Lin). www.elsevier.com/locate/ijhff International Journal of Heat and Fluid Flow 27 (2006) 436–444