Numerical Studies of Active Control of Turbulent Boundary Layers Using Transverse Travelling Waves

Turbulence control in the form of transverse wall motion is employed numerically (direct numerical simulation). Results from a turbulent boundary layer subjected to spanwise wall forcing in the form of a streamwise travelling wave are presented for the first time. Both total and phase averaging have been utilized to examine the statistical behaviour of the turbulence affected by the wall forcing. Various statistical quantities are examined and compared with results from pure temporal and spatial wall forcing. Furthermore, interesting analogies with the channel flow are discussed. INTRODUCTION The first observations of wall oscillation as means for DR was made by Jung et al. (1992) through direct numerical simulations (DNS) of a channel flow. Since then, a lot of research efforts have been made in this direction for internal flow such in a channel or pipe flow. The boundary layer flows have only recently started to be investigated numerically (Yudhistira & Skote (2011); Skote (2011, 2012, 2013, 2014); Lardeau & Leschziner (2013)), while experiments have previously been performed by quite a number of researchers. In fact, the first experimental evidence that confirmed that Jung’s DNS results was provided by Laadhari et al. (1994) and Skandaji (1997), who applied the oscillation technique to the boundary layer flow. Since then, most of the experimental investigations have been focused on the boundary layer (Trujillo et al., 1997; Choi & Clayton, 2001; Choi, 2002; Di Cicca et al., 2002; Ricco, 2004; Ricco & Wu, 2004). Extensive comparison between DNS, using the same numerical code as in the present work, and these experiments were made by Yudhistira & Skote (2011) The most commonly form of control studied is realized with a temporal wall oscillations, which is imposed through a wall velocity (W ) in the spanwise direction in the form of W =Wm sin(ωt) , (1) where Wm is the maximum wall velocity and ω is the angular frequency of the wall oscillation, which is related to the period (T ) through ω = 2π/T . The oscillation in time is relatively straightforward to implement in an experimental setting, however, a positive energy budget may not be easily obtained. Instead, researchers (Viotti et al., 2009; Skote, 2011, 2013; Negi et al., 2015) have considered a steady variation in the streamwise direction along the plate instead of a time-dependent forcing. In this case, the wall velocity (W ) is imposed in the form of